Phy5646/Another example: Difference between revisions
JorgeBarreda (talk | contribs) (New page: (Submitted by Team 1) This example was taken from "Theory and Problems of Quantum Physics", SCHAUM'S OUTLINE SERIES, p. 190-192. '''Problem:''' Consider a one dimensional harmonic oscil...) |
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The | The probability of a transition from the state n to the state k is given by | ||
:<math> | :<math> | ||
P_{nk} = \frac{1}{\hbar^2} |\int^\infty_\infty <k|V|n> e^{i t (E^{(0)}_k - E^{(0)}_n )/\hbar} dt| | |||
</math> | |||
Let e, m and w denote the charge, mass and natural frequency of the oscillator, respectively, where x denotes its deviation from its equilibrium position. In the case of an uniform field, the perturbation is given by | |||
:<math> | |||
V(x,t) = -e x \epsilon(t) - x | |||
</math> | </math> |
Revision as of 00:23, 22 April 2010
(Submitted by Team 1)
This example was taken from "Theory and Problems of Quantum Physics", SCHAUM'S OUTLINE SERIES, p. 190-192.
Problem: Consider a one dimensional harmonic oscillator embedded in a uniform electric field. The field can be considered as a small perturbation and depends on time according to
where A is constant. If the oscillator was in ground state until the field was turned on at t=0, compute in the first approximation, the probability of its excitation as a result of the action of the perturbation.
Solution:
The probability of a transition from the state n to the state k is given by
Let e, m and w denote the charge, mass and natural frequency of the oscillator, respectively, where x denotes its deviation from its equilibrium position. In the case of an uniform field, the perturbation is given by