Hyperspherical Quantum Mechanic

In the Newtonian mechanic a time is associated to each element of space. By starting from the existence of time-independent states a method where states are defined by polynomials associated with space elements and second order differential operators quantizing the states is proposed. The many body...

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Bibliographic Details
Published in:Few-body systems 2022-12, Vol.63 (4), Article 80
Main Author: Fabre de la Ripelle, M.
Format: Article
Language:English
Subjects:
Atomic
Bosons
Differential equations
Energy
Fermions
Hadrons
Heavy Ions
Molecular
Nuclear Physics
Operators (mathematics)
Optical and Plasma Physics
Particle and Nuclear Physics
Physics
Physics and Astronomy
Polynomials
Probability
Schrodinger equation
Spherical coordinates
Spherical harmonics
Wave equations
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Summary:In the Newtonian mechanic a time is associated to each element of space. By starting from the existence of time-independent states a method where states are defined by polynomials associated with space elements and second order differential operators quantizing the states is proposed. The many body wave equation is an extension of the Schrödinger equation written in polar spherical coordinates, where the Hyperspherical Potential Harmonics are substituted for spherical Harmonics. Applications to bosons and fermions systems are given.
ISSN:0177-7963
1432-5411
DOI:10.1007/s00601-022-01777-7