Abstract
In the time-dependent (TD) non-dissipative case , the information on the time-evolution of the wave.
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Notes
- 1.
Note that the phase factor \(\frac{\mathrm{i} m}{\hbar } \frac{\gamma }{4} \tilde{x}^2\) (apart from the factor \(e^{\gamma t}\) linking the physical with canonical level) corresponds to the unitary transformation between the Caldirola–Kanai approach and the one in expanding variables , as given in Eq. (4.70).
- 2.
The replacement \(V = \frac{m}{2} \omega ^2 x^2 \rightarrow \hat{V} = \frac{m}{2} \left( \omega ^2 - \frac{\gamma ^2}{4} \right) x^2\) in this position-dependent problem corresponds to the replacement \(\omega ^2 \rightarrow \left( \omega ^2 - \frac{\gamma ^2}{4} \right) \) in the TD problem Eq. (5.15) and the description in expanding variables, Eq. (4.66).
References
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Schuch, D. (2018). Dissipative Version of Time-Independent Nonlinear Quantum Mechanics. In: Quantum Theory from a Nonlinear Perspective . Fundamental Theories of Physics, vol 191. Springer, Cham. https://doi.org/10.1007/978-3-319-65594-9_6
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