Foundations of Quantum Mechanics—The Harmonic Oscillator

1979 ◽  
pp. 9-83 ◽  
Author(s):  
Arno Böhm
Keyword(s):  
Quantum Mechanics ◽  
Harmonic Oscillator ◽  
Foundations Of Quantum Mechanics

New Foundations of Quantum Mechanics

Physics Today ◽  
1966 ◽  
Vol 19 (9) ◽  
pp. 85-91 ◽  
Author(s):  
Alfred Landé ◽  
Abner Shimony
Keyword(s):  
Quantum Mechanics ◽  
Foundations Of Quantum Mechanics ◽  
New Foundations

QUANTUM SUPERSPACE, q-EXTENDED SUPERSYMMETRY AND PARASUPERSYMMETRIC QUANTUM MECHANICS

1993 ◽  
Vol 08 (28) ◽  
pp. 2657-2670 ◽  
Author(s):  
K. N. ILINSKI ◽  
V. M. UZDIN
Keyword(s):  
Quantum Mechanics ◽  
Extended Supersymmetry ◽  
Harmonic Oscillator ◽  
Unit Circle ◽  
Canonical Quantization ◽  
Matrix Representations ◽  
Dimensional Matrix ◽  
Continuous Parameter ◽  
Superspace Formalism

We describe q-deformation of the extended supersymmetry and construct q-extended supersymmetric Hamiltonian. For this purpose we formulate q-superspace formalism and construct q-supertransformation group. On this basis q-extended supersymmetric Lagrangian is built. The canonical quantization of this system is considered. The connection with multi-dimensional matrix representations of the parasupersymmetric quantum mechanics is discussed and q-extended supersymmetric harmonic oscillator is considered as a simplest example of the described constructions. We show that extended supersymmetric Hamiltonians obey not only extended SUSY but also the whole family of symmetries (q-extended supersymmetry) which is parametrized by continuous parameter q on the unit circle.

scholarly journals Epistemic Horizons and the Foundations of Quantum Mechanics

2018 ◽  
Vol 48 (12) ◽  
pp. 1669-1697 ◽  
Author(s):  
Jochen Szangolies
Keyword(s):  
Quantum Mechanics ◽  
Foundations Of Quantum Mechanics
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