This preview shows pages 1–2. Sign up to view the full content.
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
Unformatted text preview: A particle with mass m is trapped in a simple harmonic oscillator potential with resonance frequency ω , and is prepared at time t = 0 in the (not normalized) state ψ ( x, 0) = N (2 ψ ( x )iψ 1 ( x )) , (3) where ψ and ψ 1 are the ground and ﬁrst excited eigenstates of the harmonic oscillator, which are given by the normalized expressions ψ ( x ) = ± mω π ¯ h ¶ 1 / 4 eζ 2 / 2 (4) and ψ 1 ( x ) = ± mω π ¯ h ¶ 1 / 4 √ 2 ζeζ 2 / 2 , (5) where ζ = q mω / ¯ h x . (a) [5 points] Find the normalization N . (b) [5 points] Find the expectation value for the energy. (c) [5 points] Work out the time dependence for ψ ( x,t ). (c) [10 points] Work out how long you have to wait for ψ ( x,t ) to return to the initial state ψ ( x, 0), ignoring any overall complex phase factors of the form e iφ ....
View
Full
Document
This note was uploaded on 03/01/2009 for the course PHYS 115A taught by Professor Nelson during the Spring '03 term at UCSB.
 Spring '03
 Nelson
 Physics, mechanics

Click to edit the document details