The gauge-invariant formulation of quantum mechanics is compared to the conventional approach for the case of a one-dimensional charged harmonic oscillator in an electromagnetic field in the electric dipole approximation. The probability of finding the oscillator in the ground state or excited states as a function of time is calculated, and the two approaches give different results. On the basis of gauge invariance, the gauge-invariant formulation of quantum mechanics gives the correct probability, while the conventional approach is incorrect for this problem. Therefore, expansion coefficients or a wave function cannot always be interpreted as probability amplitudes. For a physical interpretation as probability amplitudes the expansion coefficients must be gauge invariant.
| Identifer | oai:union.ndltd.org:unt.edu/info:ark/67531/metadc504158 |
| Date | 08 1900 |
| Creators | Wen, Chang-tai |
| Contributors | Kobe, Donald Holm, Redding, Rogers W., Deering, William D. |
| Publisher | North Texas State University |
| Source Sets | University of North Texas |
| Language | English |
| Detected Language | English |
| Type | Thesis or Dissertation |
| Format | v, 103 leaves: ill., Text |
| Rights | Public, Wen, Chang-tai, Copyright, Copyright is held by the author, unless otherwise noted. All rights reserved. |
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