Quaternion supersymmetric quantum mechanics and SWKB approximation

A theory of quaternionic supersymmetric quantum mechanics has been developed in terms of quaternion supercharges, superpartner Hamiltonian and energy eigenvalues. We have obtained higher-order Hamiltonians with the help of lowering/raising quaternion operators and superpartner Hamiltonians, so one c...

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Bibliographic Details
Published in:European physical journal plus 2022-06, Vol.137 (6), p.660, Article 660
Main Authors: Rawat, Seema, Rawat, A. S.
Format: Article
Language:English
Subjects:
Applied and Technical Physics
Approximation
Atomic
Complex Systems
Condensed Matter Physics
Dark matter
Eigenvalues
Energy
Hamiltonian functions
Mathematical analysis
Mathematical and Computational Physics
Molecular
Optical and Plasma Physics
Physics
Physics and Astronomy
Quantum mechanics
Quantum physics
Quaternions
Regular Article
Supersymmetry
Theoretical
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Summary:A theory of quaternionic supersymmetric quantum mechanics has been developed in terms of quaternion supercharges, superpartner Hamiltonian and energy eigenvalues. We have obtained higher-order Hamiltonians with the help of lowering/raising quaternion operators and superpartner Hamiltonians, so one can arrive at higher-dimensional theories from lower dimensions by using this technique. It has been shown that partner Hamiltonians contain many terms which can indicate the presence of an extra particle, dark matter, or any unanswered physics phenomenon. Supersymmetric WKB approximation has also been tested in the quaternion space for superpotentials V + and V -, and it is concluded that the SWKB quantization condition in quaternion space is not exact and is slightly different from the usual SWKB quantization condition.
ISSN:2190-5444
2190-5444
DOI:10.1140/epjp/s13360-022-02884-4