Phy5646/Simpe Example of Time Dep Pert: Difference between revisions
Jump to navigation
Jump to search
No edit summary |
No edit summary |
||
| Line 3: | Line 3: | ||
'''Problem:''' A particle of charge <math>q</math> in a one-dimensional harmonic oscillator of characteristic frequency <math>\omega</math> is placed in an electric field that is turned on and off so that the potential energy is | '''Problem:''' A particle of charge <math>q</math> in a one-dimensional harmonic oscillator of characteristic frequency <math>\omega</math> is placed in an electric field that is turned on and off so that the potential energy is | ||
<math>\lambda V(t) | <math>\lambda V(t) = qExe^{-t^{2}/\tau^{2}}</math> | ||
If the particle is initially in the ground state, what is the probability that after time t, such that t >£> t, | |||
the particle is found in the first excited state of the harmonic oscillator? What is the probability that | |||
it is found in the second excited state? | |||
Revision as of 00:57, 28 March 2010
This example taken from "Quantum Physics" 3rd ed., Stephen Gasiorowicz, p. 237-238.
Problem: A particle of charge in a one-dimensional harmonic oscillator of characteristic frequency is placed in an electric field that is turned on and off so that the potential energy is
If the particle is initially in the ground state, what is the probability that after time t, such that t >£> t, the particle is found in the first excited state of the harmonic oscillator? What is the probability that it is found in the second excited state?