Formulation of general dynamical invariants and their unitary relations
for time-dependent three coupled quantum oscillators
- URL: http://arxiv.org/abs/2212.07643v1
- Date: Thu, 15 Dec 2022 07:30:18 GMT
- Title: Formulation of general dynamical invariants and their unitary relations
for time-dependent three coupled quantum oscillators
- Authors: Jeong Ryeol Choi
- Abstract summary: A general invariant operator for three coupled time-dependent oscillators is derived.
The invariant operator and its eigenfunctions can be used to characterize quantum properties of the systems.
- Score: 0.0
- License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
- Abstract: A general dynamical invariant operator for three coupled time-dependent
oscillators is derived. Although the obtained invariant operator satisfies the
Liouville-von Neumann equation, its mathematical formula is somewhat
complicated due to arbitrariness of time variations of parameters. The
parametric conditions required for formulating this invariant are definitely
specified. By using the unitary transformation method, the invariant operator
is transformed to the one that corresponds to three independent simple harmonic
oscillators. Inverse transformation of the well-known quantum solutions
associated with such a simplified invariant enables us to identify quantum
solutions of the coupled original systems. These solutions are exact since we
do not use approximations not only in formulating the invariant operator but in
the unitary transformation as well. The invariant operator and its
eigenfunctions provided here can be used to characterize quantum properties of
the systems with various choices of the types of time-dependent parameters.
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