
Summary: We use an invariant operator to obtain the Schrödinger solution of damped-amplified oscillators. The expectation values of the quantum mechanical energy operator correspond to the classical energy. The geometric phase of the system increases linearly with time. We confirm that the uncertainty principle always holds. The uncertainty relation in coherent state is the same as the minimum value of that in number state.
Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics, Differential geometric methods, including holonomy, Berry and Hannay phases, Aharonov-Bohm effect, etc. in quantum theory
Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics, Differential geometric methods, including holonomy, Berry and Hannay phases, Aharonov-Bohm effect, etc. in quantum theory
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