ps06 - Homework(6 for Physics 316 Modern Physics...

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: Homework (6) for Physics 316, Modern Physics I (Hoffstaetter/Drasco/Thibault) Due Date: Friday, 03/11/05 - 9:55 in 132 Rockefeller Hall Exercise 1: Compute the position uncertainty Δ x in the ground state Φ ( x ) = 1 p √ πa e- ξ 2 2 , ξ = x a , a = r ~ mω . (1) for the harmonic oscillator potential. Use Δ x = p < ( x- < x > ) 2 > = √ < x 2 >- < x > 2 and the expectation values < x > = Z ∞-∞ x | Φ ( x ) | 2 dx , < x 2 > = Z ∞-∞ x 2 | Φ ( x ) | 2 dx . (2) Exercise 2: What is the expectation value h V i and the uncertainty Δ V = p h V 2 i-h V i 2 of the harmonic oscillator potential V = 1 2 mω 2 x 2 for the ground state wave function? Show that also for any other stationary state Φ n , h V i is half the energy E n = ~ ω ( n + 1 2 ). This corresponds to the fact that the energy of a classical harmonic oscillator is on average split in equal parts between kinetic an potential energy....
View Full Document

This note was uploaded on 09/28/2008 for the course PHYS 316 taught by Professor Hoffstaetter during the Spring '05 term at Cornell.

Ask a homework question - tutors are online