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## Aproximação na esfera por uma soma com pesos de harmônicos esféricos; Approximation on the sphere by weighted sums of spherical harmonics

Piantella, Ana Carla
Fonte: Biblioteca Digitais de Teses e Dissertações da USP Publicador: Biblioteca Digitais de Teses e Dissertações da USP
Tipo: Tese de Doutorado Formato: application/pdf
Publicado em 08/03/2007 PT
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O objetivo deste trabalho é estudar aproximação na esfera por uma soma com pesos de harmônicos esféricos. Apresentamos condições necessárias e suficientes sobre os pesos para garantir a convergência, tanto no caso contínuo quanto no caso Lp. Analisamos a ordem de convergência dos processos aproximatórios usando um módulo de suavidade esférico relacionado à derivada forte de Laplace-Beltrami. Incluímos provas para vários resultados sobre a derivada forte de Laplace-Beltrami, já que não conseguimos encontrá-las na literatura; The subject of this work is to study approximation on the sphere by weighted sums of spherical harmonics. We present necessary and sufficient conditions on the weights for convergence in both, the continuous and the Lp cases. We analyse the convergence rates of the approximation processes using a modulus of smoothness related to the strong Laplace- Beltrami derivative. We include proofs for several results related to such a derivative, since we were unable to find them in the literature

## A harmônica na antiguidade grega; Harmonics in greek antiquity

Gusmão, Cynthia Sampaio de
Fonte: Biblioteca Digitais de Teses e Dissertações da USP Publicador: Biblioteca Digitais de Teses e Dissertações da USP
Tipo: Dissertação de Mestrado Formato: application/pdf
Publicado em 22/04/2010 PT
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principais teorias acerca do som musical na Antiguidade grega, entre o final do século VI a.C. e o início do século III a.C. O estudo analisa, em primeiro lugar, as circunstâncias históricas e materiais que propiciaram o desenvolvimento da teoria musical grega, chamada harmônica, e a sua relação com a prática musical do período em questão. A primeira teoria analisada está inserida no contexto da escola pitagórica, em que a cosmologia é o referencial de uma visão de mundo que se expande conectando todas as áreas do pensamento, e um dos pontos de origem é a harmônica matemática. São apresentadas a seguir as demonstrações feitas a partir do cálculo das médias proporcionais e sua relação com o princípio da coesão harmônica da oitava. No segundo capítulo são estudadas as teorias acústicas da Antiguidade, que se originaram das razões pitagóricas e se desenvolveram no âmbito das ciências naturais, aprofundando-se com a filosofia aristotélica. No terceiro capítulo, são analisados os principais pontos de confronto promovidos pela corrente aristoxeniana, que se insere no quadro epistemológico aristotélico, e que foram levantados contra os pitagóricos. Nessa nova forma de pensamento, a harmônica é estudada como uma tékne...

## DC and AC side harmonics in CCC converters

Oliveira, Luis C. Origa de; Borges, Wilson M.; Souza, Julio B. de; Ravagnani, Lidia L.
Fonte: IEEE Publicador: IEEE
Tipo: Conferência ou Objeto de Conferência Formato: 245-249
ENG
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The capacitor-commutated converter (CCC) has frequently been used in the conception of HVDC systems connected to busbars with low short circuit level. This alternative arrangement, in substitution to the conventional ones, guarantees less sensitive operational conditions to problems related with the commutation failure in the inverters besides supplying part of the reactive energy to be compensated. Studies related with its performance in steady and transient states have been presented in several works, however its behavior as harmonic source is still little explored. This work presents preliminary studies focusing the generation of characteristic harmonics by this type of converter. Subjects related with the amplification of the harmonic magnitudes are investigated and compared considering similar arrangements of conventional static converters (LCC) and CCC schemes. It is also analyzed the harmonic generation on the dc side of the installation and its influence on the ac side harmonics. The results are obtained from simulations in the time domain in PSpice environment and they clearly illustrate the operational differences between the L CC and the CCC schemes with regard to characteristic harmonic generation.

## Single-phase series active conditioner for the compensation of voltage harmonics, sags, swell and flicker

Carneiro, H.; Pinto, J. G.; Afonso, João L.
Fonte: Universidade do Minho Publicador: Universidade do Minho
Tipo: Artigo de Revista Científica
Publicado em /06/2011 ENG
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Simulation and experimental results shown on this paper describes the performance of a developed Single-Phase Series Active Conditioner that regulates the voltage being delivered to a load. This Custom Power device is a solution for power quality issues related with voltage amplitude variations, which are responsible for innumerous flaws in industrial processes which brings with it high financial losses. The Single-Phase Series Active Conditioner is a back-to-back converter, composed by two power converters sharing a common DC link. One of the converters is series connected to the electrical grid, whereas the other one is shunt connected. The first is used to compensate load voltage, and the second to regulate the DC link voltage. This paper shows the results obtained with the Series Active Conditioner in Sag, Swell and Flicker events, and also Voltage Harmonics compensation, in order to deliver to the load a sinusoidal voltage, at nominal amplitude.; Fundação para a Ciência e Tecnologia (FCT)

## Can temporal fine structure represent the fundamental frequency of unresolved harmonics?

Oxenham, Andrew J.; Micheyl, Christophe; Keebler, Michael V.
Fonte: Acoustical Society of America Publicador: Acoustical Society of America
Tipo: Artigo de Revista Científica
Publicado em /04/2009 EN
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At least two modes of pitch perception exist: in one, the fundamental frequency (F0) of harmonic complex tones is estimated using the temporal fine structure (TFS) of individual low-order resolved harmonics; in the other, F0 is derived from the temporal envelope of high-order unresolved harmonics that interact in the auditory periphery. Pitch is typically more accurate in the former than in the latter mode. Another possibility is that pitch can sometimes be coded via the TFS from unresolved harmonics. A recent study supporting this third possibility [Moore et al. (2006a). J. Acoust. Soc. Am. 119, 480–490] based its conclusion on a condition where phase interaction effects (implying unresolved harmonics) accompanied accurate F0 discrimination (implying TFS processing). The present study tests whether these results were influenced by audible distortion products. Experiment 1 replicated the original results, obtained using a low-level background noise. However, experiments 2–4 found no evidence for the use of TFS cues with unresolved harmonics when the background noise level was raised, or the stimulus level was lowered, to render distortion inaudible. Experiment 5 measured the presence and phase dependence of audible distortion products. The results provide no evidence that TFS cues are used to code the F0 of unresolved harmonics.

## A simulation study of harmonics regeneration in noise reduction for electric and acoustic stimulation

Hu, Yi
Fonte: Acoustical Society of America Publicador: Acoustical Society of America
Tipo: Artigo de Revista Científica
Publicado em /05/2010 EN
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Recent research results show that combined electric and acoustic stimulation (EAS) significantly improves speech recognition in noise, and it is generally established that access to the improved F0 representation of target speech, along with the glimpse cues, provide the EAS benefits. Under noisy listening conditions, noise signals degrade these important cues by introducing undesired temporal-frequency components and corrupting harmonics structure. In this study, the potential of combining noise reduction and harmonics regeneration techniques was investigated to further improve speech intelligibility in noise by providing improved beneficial cues for EAS. Three hypotheses were tested: (1) noise reduction methods can improve speech intelligibility in noise for EAS; (2) harmonics regeneration after noise reduction can further improve speech intelligibility in noise for EAS; and (3) harmonics sideband constraints in frequency domain (or equivalently, amplitude modulation in temporal domain), even deterministic ones, can provide additional benefits. Test results demonstrate that combining noise reduction and harmonics regeneration can significantly improve speech recognition in noise for EAS, and it is also beneficial to preserve the harmonics sidebands under adverse listening conditions. This finding warrants further work into the development of algorithms that regenerate harmonics and the related sidebands for EAS processing under noisy conditions.

## Computation of higher order ellipsoidal harmonics with an application in electroencephalography

Dassios, George; Chatjigeorgiou, Ioannis K.
Fonte: Oxford University Press Publicador: Oxford University Press
Tipo: Artigo de Revista Científica Formato: text/html
EN
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A triaxial ellipsoid provides an approximation of the average human brain which is much better than the broadly used spherical model. The theoretical solution of the forward problem of the Electroencephalography with an isolated dipolar source has been already derived and reported in the literature. This solution is expressed in terms of an eigenexpansion in ellipsoidal harmonics. Nevertheless, this expression was not possible to be handled effectively since no ellipsoidal harmonics of degree higher than three were available in closed forms. In order to analyze further this problem an effective algorithm has been developed, which generates the ellipsoidal harmonics of arbitrary degree and order in a numerical form. The algorithm has been compared with the known analytical eigenfunctions and the results manifested a perfect coincidence. Finally, this algorithm was used to construct a numerically stable solution of the electric potential on the surface of the head, which is generated by a single dipole of arbitrary position and orientation. The degree of ellipsoidal harmonics needed for a numerically convergent solution goes all the way up to 30. The objectives of the present work are twofold. The first objective concerns the development of a numerical algorithm that can produce Lamé functions and ellipsoidal harmonics of any finite degree. Then this algorithm is utilized to generate the electric potential on the boundary of the ellipsoidal brain-head system. This application is a direct theoretical realization of the brain imagine modality known as Electroencephalography. We demonstrate...

## Atenuação de harmônicos nos geradores síncronos provenientes das cargas não lineares utilizando geradores de indução; Attenuation of harmonics on synchronous generators arising from nonlinear loads using induction generators

Delbone, Edval
Fonte: Universidade Federal de Uberlândia Publicador: Universidade Federal de Uberlândia
Tipo: Tese de Doutorado
POR
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Este trabalho demonstra a viabilidade teórica e experimental de um gerador de indução funcionar como um atenuador dos harmônicos nos geradores principais do sistema elétrico de potência, ou seja, os geradores síncronos. Foram analisadas as máquinas de indução e síncronas do ponto de vista físico e estabelecidas modelagens matemáticas no domínio da frequência, a fim de comprovar o objetivo da tese. Foram realizadas também´em, simulações computacionais no domínio do tempo e ensaios em laboratório para verificar os n´níveis de atenuação de harmônicos de corrente (THDi) em conformidade com os limites máximos de distorções harmônicas de tensão (THDv) normalizados. Apresenta-se também neste trabalho um estudo de viabilidade técnica e econômica de uma aplicação típica. ______________________________________________________________________________ ABSTRACT; This work demonstrates the theoretical and experimental feasibility of a induction generator to work as an attenuator of the harmonics in main generators of on the electric power system, i.e., the synchronous generators. The induction and synchronous machines were analyzed in physical terms and established mathematical modeling in the frequency domain in order to prove the purpose of the thesis. Computer simulations were also carried out in the time domain and laboratory tests were made to check levels of attenuation of current harmonics (THDi) in accordance with the maximum standardized voltage harmonic distortion (THDv). Furthermore...

## Experimental guided spherical harmonics based head-related transfer function modeling

Zhang, Mengqiu
Fonte: Universidade Nacional da Austrália Publicador: Universidade Nacional da Austrália
Tipo: Thesis (PhD); Doctor of Philosophy (PhD)
EN_AU
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In this thesis we investigate the experimental guided spherical harmonics based Head-Related Transfer Function (HRTF) modeling where HRTFs are parameterized as frequency and source location. We focus on efficiently representing the HRTF variations in sufficient detail by mathematical modeling and the experimental measurements. The goal of this work is towards an optimal functional HRTF modeling taking into account the demands of decreasing the computational cost and alleviating the HRTF interpolation and/or extrapolation in the headphone based binaural systems. To represent HRTF by models, we firstly consider the high variability of HRTFs among individuals caused by the differentiation of the scattering effects of the individual bodies on the sound waves. We conduct a series of statistical analyses on an experimental HRTF database of human subjects to reveal the correlation between the physical features of human beings, especially pinna, head, and torso, and the corresponding HRTFs. The strategy enables us to identify a minimal set of physical features which strongly influence the HRTFs in a direct physical way. We next consider the continuity of the HRTF representation in both spatial and frequency domain. We define a functional HRTF model class in which the HRTF spatial representation has been justified to be well approximated by a finite number of spherical harmonics while HRTF frequency representation remains the focus of this thesis. In order to seek an efficient representation for HRTF frequency portion...

## High harmonics generation from excited states of atomic lithium

Ivanov, Igor; Kheifets, Anatoli
Fonte: Institute of Physics Publishing Publicador: Institute of Physics Publishing
Tipo: Artigo de Revista Científica
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We present a calculation of the harmonics yield from the lithium atom exposed to an intense 3.5 νm mid-infrared laser pulse. Our calculation shows that a considerable increase of the yield of high harmonics generation (HHG) can be achieved if initially t

## Negative refractive index and higher-order harmonics in layered metallodielectric optical metamaterials

Maas, Ruben; Verhagen, Ewold; Parsons, James; Polman, Albert
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Publicado em 18/04/2014
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We study the propagation of light in a three-dimensional double-periodic Ag/TiO2 multilayer metamaterial composed of coupled plasmonic waveguides operating in the visible and UV spectral range. For these frequencies, light propagation in the plane of the waveguides is described by a negative phase velocity, while for the orthogonal direction light propagation is described by a Bloch wave composed of a large number of harmonics. As a result, the material cannot generally be described by a single phase index: decomposing the Bloch wave into different harmonics we show that for the wavelength range of interest the positive index m=1 harmonic dominates the propagation of light in the orthogonal direction. These results are corroborated by numerical simulations and optical refraction experiments on a double-periodic Ag/TiO2 multilayer metamaterial prism in the 380-600 nm spectral range, which show that positive refraction associated with right-handed harmonics dominates. Studying the isofrequency contours we find that despite the occurrence of multiple harmonics the double-periodic structure can act as a flat lens: for a slab consisting of an integer number of unit cells all harmonics are degenerate and constructively interfere at the image plane. This work identifies important considerations relevant to the design of many three dimensional periodic metamaterials.; Comment: 11 pages...

## Generation of Higher-Order Harmonics By Addition of a High Frequency XUV Radiation to the IR One

Fleischer, Avner; Moiseyev, Nimrod
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Publicado em 01/02/2008
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The irradiation of atoms by a strong IR laser field of frequency $\omega$ results in the emission of odd-harmonics of $\omega$ ("IR harmonics") up to some maximal cut-off frequency. The addition of an XUV field of frequency $\tilde{q}\omega$ larger than the IR cut-off frequency to the IR driver field leads to the appearance of new higher-order harmonics ("XUV harmonics") $\tilde{q} \pm 2K, 2\tilde{q} \pm (2K-1), 3\tilde{q} \pm 2K,...$ ($K$ integer) which were absent in the spectra in the presence of the IR field alone. The mechanism responsible for the appearance of the XUV harmonics is analyzed analytically using a generalization of the semiclassical re-collision (three-step) model of high harmonic generation. It is shown that the emitted HHG radiation field can be written as a serie of terms, with the HHG field obtained from the three-step model in its most familiar context [P. B. Corkum, \textit{Phys. Rev. Lett.} {\bf 71}, 1994 (1993)] resulting from the zeroth-order term. The origin of the higher-order terms is shown to be the ac-Stark oscillations of the remaining ground electronic state which are induced by the XUV field. These terms are responsible for the appearance of the new XUV harmonics in the HGS. The XUV harmonics are formed by the same electron trajectories which form the IR harmonics and have the same emission times...

## Some remarks on spherical harmonics

Gichev, V. M.
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
RU
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The article contains several observations on spherical harmonics and their nodal sets: a construction for harmonics with prescribed zeroes; a kind of canonical representation of this type for harmonics on $\bbS^2$; upper and lower bounds for nodal length and inner radius (the upper bounds are sharp); precise upper bound for the number of common zeroes of two spherical harmonics on $\bbS^2$; the mean Hausdorff measure on the intersection of $k$ nodal sets for harmonics of different degrees on $\bbS^m$, where $k\leq m$ (in particular, the mean number of common zeroes of $m$ harmonics).; Comment: 20 pages. Translation of the version which is published in Russian. Minor modifications throughout the paper. An error in calculation is corrected (page 14)

## Analyzing Correlation Functions with Tesseral and Cartesian Spherical Harmonics

Danielewicz, Pawel; Pratt, Scott
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
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The dependence of inter-particle correlations on the orientation of particle relative-momentum can yield unique information on the space-time features of emission in reactions with multiparticle final states. In the present paper, the benefits of a representation and analysis of the three-dimensional correlation information in terms of surface spherical harmonics is presented. The harmonics include the standard complex tesseral harmonics and the real cartesian harmonics. Mathematical properties of the lesser-known cartesian harmonics are illuminated. The physical content of different angular harmonic components in a correlation is described. The resolving power of different final-state effects with regarding to determining angular features of emission regions is investigated. The considered final-state effects include identity interference and strong and Coulomb interactions. The correlation analysis in terms of spherical harmonics is illustrated with the cases of gaussian and blast-wave sources for proton-charged meson and baryon-baryon pairs.; Comment: 32 pages 10 figures

## Computational science and re-discovery: open-source implementations of ellipsoidal harmonics for problems in potential theory

Bardhan, Jaydeep P.; Knepley, Matthew G.
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
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We present two open-source (BSD) implementations of ellipsoidal harmonic expansions for solving problems of potential theory using separation of variables. Ellipsoidal harmonics are used surprisingly infrequently, considering their substantial value for problems ranging in scale from molecules to the entire solar system. In this article, we suggest two possible reasons for the paucity relative to spherical harmonics. The first is essentially historical---ellipsoidal harmonics developed during the late 19th century and early 20th, when it was found that only the lowest-order harmonics are expressible in closed form. Each higher-order term requires the solution of an eigenvalue problem, and tedious manual computation seems to have discouraged applications and theoretical studies. The second explanation is practical: even with modern computers and accurate eigenvalue algorithms, expansions in ellipsoidal harmonics are significantly more challenging to compute than those in Cartesian or spherical coordinates. The present implementations reduce the "barrier to entry" by providing an easy and free way for the community to begin using ellipsoidal harmonics in actual research. We demonstrate our implementation using the specific and physiologically crucial problem of how charged proteins interact with their environment...

## Avaluació d'una proposta didàctica per a la identificació auditiva dels intervals harmònics musicals. Una experimentació al primer curs dels ensenyaments especialitzats de grau professional dels conservatoris de música de Catalunya

Ponsatí Ferrer, Imma
Fonte: [Barcelona] : Universitat Autònoma de Barcelona, Publicador: [Barcelona] : Universitat Autònoma de Barcelona,
Tipo: Tesis i dissertacions electròniques; info:eu-repo/semantics/doctoralThesis; info:eu-repo/semantics/publishedVersion Formato: application/pdf
Publicado em //2011 CAT
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L'objectiu general d'aquesta tesi és elaborar, experimentar i avaluar una proposta didàctica per a la identificació auditiva dels intervals harmònics adreçada al primer curs dels ensenyaments musicals de grau professional dels conservatoris de música de Catalunya i que, a partir de la detecció i anàlisi prèvia de les dificultats dels alumnes, permeti que aquests assoleixin, al llarg del procés d'ensenyament-aprenentatge, els objectius didàctics plantejats i, conseqüentment, al final d'aquest, millorin el seu rendiment. En el marc teòric es revisen, analitzen i sintetitzen els principals escrits sobre l'objecte d'estudi de la recerca, els quals han servit de referència per a la seva elaboració. D'una banda, s'han recollit les aportacions dels autors més significatius i, de l'altra, efectuat reflexions personals sobre els temes exposats: es fa una aproximació a la importància que té l'oïda musical al llarg del procés de formació dels estudiants de música; ens apropem a l'oïda musical melòdica, polifònica i harmònica, totes elles considerades dins del context de la tonalitat; s'entra de ple a revisar les principals recerques centrades en la identificació auditiva dels intervals harmònics musicals; s'exposen les línies generals que regeixen els estudis musicals de grau elemental...

## Properties of the spectra of asymmetric molecules: matrix evaluation in bases of spherical harmonics and common generating function

Ley-Koo,E; Méndez-Fragoso,R
Fonte: Sociedad Mexicana de Física Publicador: Sociedad Mexicana de Física
Tipo: Artigo de Revista Científica Formato: text/html
Publicado em 01/02/2008 EN
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The Schrodinger equation for the rotational states of asymmetric molecules is known to be separable in spheroconal coordinates and integrable in terms of Lame functions. However, the numerical evaluation of the latter has not been developed efficiently, thereby limiting the practical application of such solutions. In this article, the matrix evaluation of the rotational states is formulated and implemented numerically for any asymmetric molecule, using the familiar bases of spherical harmonics. The matrix of the Hamiltonian - in a frame of reference fixed in the molecule and oriented along its principal axes - is constructed in the chosen basis and shown to separate into blocks of (+1) ×(+1) and ×for each value of the angular momentum quantum number . The diagonalization of the successive blocks leads to accurate values of eigenenergies and eigenvectors for all values of the asymmetry parameters. The connection between these rotational states and their Lame function representation is also established...

## Spin-weighted spherical harmonics and their applications

Torres del Castillo,G. F
Fonte: Sociedad Mexicana de Física Publicador: Sociedad Mexicana de Física
Tipo: Artigo de Revista Científica Formato: text/html
Publicado em 01/02/2007 EN
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A brief introduction to the spin-weighted spherical harmonics is given, and some applications of these functions in the solution by separation of variables of various systems of partial differential equations are presented. The examples considered here are the source-free Maxwell equations in flat space-time and in the Schwarzschild space-time, the Einstein vacuum field equations linearized about the flat space-time and the Dirac equation.

## A generating function for the spherical harmonics in p dimensions

Torres del Castillo,G.F.
Fonte: Sociedad Mexicana de Física Publicador: Sociedad Mexicana de Física
Tipo: Artigo de Revista Científica Formato: text/html
Publicado em 01/06/2013 EN
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A generating function for the spherical harmonics in three or more dimensions is given. This function allows us to find in a simple manner the explicit expressions for the spherical harmonics in three dimensions. The generating functions for the spherical harmonics given here are analogous to certain well-known generating functions for solutions of the wave equation.

## The hydrogen atom via the four-dimensional spherical harmonics

Torres del Castillo,G.F.; Calvario Acócal,J.L.
Fonte: Sociedad Mexicana de Física Publicador: Sociedad Mexicana de Física
Tipo: Artigo de Revista Científica Formato: text/html
Publicado em 01/10/2007 EN
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Using the fact that the Schrödinger equation for the stationary states of the hydrogen atom is equivalent to an integral equation on the unit sphere in a four-dimensional space, the eigenvalues, the eigenfunctions, and a dynamical symmetry group for this problem are obtained from the four-dimensional spherical harmonics and the group of rotations on the sphere. It is shown that the four-dimensional spherical harmonics separable in Euler angles correspond to solutions of the time-independent Schrödinger equation that are separable in parabolic coordinates.