Linear invariants of a time-dependent quantal oscillator

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Abstract
Explicitly time‐dependent invariants, linear in x and p, are found to simplify the solution of the Schrödinger equation with oscillator‐type Hamiltonian. As an example, exact dynamics is obtained of the time‐dependent quantal oscillator, with damping and subject to external force. The invariant and hence the solution of the Schrödinger equation involve only the amplitude of the classical damped oscillator. The identity of our solution with a recently obtained result is illustrated. A digressive remark on quadratic invariants and the Dirac operator formalism is added.