On the Schrödinger-Langevin Equation
It is shown that the Heisenberg-Langevin equation can be used to derive a Schrödinger equation for a Brownian particle interacting with a thermal environment. The equation derived is iℏ(∂ψ/∂ t)=−(ℏ2/2m)∇2ψ+Vψ+VRψ+[(ℏ f/2im) ln(ψ/ψ*)+W(t)]ψ(r, t), W(t)=−(ℏ f/2im)∫ψ* ln(ψ/ψ*)ψ dr,where f is t...
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| Veröffentlicht in: | The Journal of chemical physics 1972-11, Vol.57 (9), p.3589-3591 |
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| Format: | Artikel |
| Sprache: | eng |
| Online-Zugang: | Volltext |
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| Zusammenfassung: | It is shown that the Heisenberg-Langevin equation can be used to derive a Schrödinger equation for a Brownian particle interacting with a thermal environment. The equation derived is iℏ(∂ψ/∂ t)=−(ℏ2/2m)∇2ψ+Vψ+VRψ+[(ℏ f/2im) ln(ψ/ψ*)+W(t)]ψ(r, t), W(t)=−(ℏ f/2im)∫ψ* ln(ψ/ψ*)ψ dr,where f is the friction constant and VR is a random potential. |
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| ISSN: | 0021-9606 1089-7690 |
| DOI: | 10.1063/1.1678812 |