An Exact Quantum Theory of the Time‐Dependent Harmonic Oscillator and of a Charged Particle in a Time‐Dependent Electromagnetic Field

1969 ◽  
Vol 10 (8) ◽  
pp. 1458-1473 ◽  
Author(s):  
H. R. Lewis ◽  
W. B. Riesenfeld
Keyword(s):  
Electromagnetic Field ◽  
Quantum Theory ◽  
Charged Particle ◽  
Harmonic Oscillator ◽  
Time Dependent ◽  
Exact Quantum

Exact quantum theory of a time-dependent bound quadratic Hamiltonian system

1993 ◽  
Vol 48 (4) ◽  
pp. 2716-2720 ◽  
Author(s):  
Kyu Hwang Yeon ◽  
Kang Ku Lee ◽  
Chung In Um ◽  
Thomas F. George ◽  
Lakshmi N. Pandey
Keyword(s):  
Quantum Theory ◽  
Hamiltonian System ◽  
Time Dependent ◽  
Exact Quantum ◽  
Quadratic Hamiltonian

Comment on: Quantum theory of a non-Hermitian time-dependent forced harmonic oscillator having 𝒫𝒯 symmetry

2020 ◽  
Vol 35 (01) ◽  
pp. 2075001
Author(s):  
Naima Mana ◽  
Mustapha Maamache
Keyword(s):  
Quantum Theory ◽  
Harmonic Oscillator ◽  
External Force ◽  
Time Dependent ◽  
Normalization Condition ◽  
Complex Time ◽  
Linear Invariant ◽  
Novel Concept

Pedrosa et al.1 have recently used a [Formula: see text] symmetric linear invariant to study a unidimensional time-dependent [Formula: see text] symmetric harmonic oscillator with a complex time-dependent [Formula: see text] symmetric external force. We show in this comment that the normalization condition of the eigenfunctions of the invariant is not verified as claimed in Ref. 1. In order to obtain the normalization condition, we introduce a novel concept of the pseudoparity-time (pseudo-[Formula: see text]) symmetry.

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