Gauge Invariance of a Time-Dependent Harmonic Oscillator in Magnetic Dipole Approximation

Donald H. Kobe, Edward C. -T. Wen

Qian Shang-Wu, Wang Jing-Shan

A manifestly gauge-invariant formulation of non-relativistic quantum mechanics is applied to the case of time-dependent harmonic oscillator in the magnetic dipole approximation. A general equation for obtaining gauge-invariant transition probability amplitudes is derived.

Ettore Salusti B, Francesco Zirilli

Qian Shang-Wu

A manifestly gauge-invariant formulation of non-relativistic quanturn mechanics is applied to the case of time-dependent harmonic oscillator in the magnetic dipole approximation.A general equation for obtaining gauge invariant transition probability amplitudes is derived.

B. Bassetti, E. Montaldi, Mario Raciti

Paul K. Kennedy, Donald H. Kobe

A manifestly gauge-invariant formulation of quantum mechanics is applied to a charged isotropic harmonic oscillator in a time-varying magnetic field in the magnetic dipole approximation. The energy operator for the problem is the sum of the kinetic and potential energies. The kinetic energy operator is the square of the gauge-invariant kinetic momentum operator divided by twice the mass. The energy eigenvalues and state probabilities are calculated and are shown to be the same in all gauges. In this problem there is no gauge in which the energy operator reduces to the unperturbed Hamiltonian, as there is in the electric dipole approximation. Consequently, eigenvalues of the unperturbed Hamiltonian and corresponding (gauge-dependent) state 'probabilities' are different from the gauge-invariant quantities in all gauges.