Chapter 7 Problem Solutions

# 44b m w 14 y0 hxl i p m m w x2 2 the energy of this

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

This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: t + dL cn Therefore Xx\ = A cosHw t + dL X px \ = -m w A sinHw t + dL A = 2 — Hn + 1L ê H2 m wL d = Arg Hcn L - Arg Hcn + 1 L where cn cn + 1 and so „ „t „ „t X px \ Xx\ = m X px \ = -m w2 Xx\ which are the Ehrenfest relations. Problem 7.13 The position-space wavefunction of the harmonic oscillator ground state is given by (7.44b) m w 1ê4 y0 HxL = I p — M ‰ - m w x2 2— The energy of this state is E0 = — w ê 2, so the classically disallowed region is that for which V HxL > E0 1 2 m w2 x2 > x > —w 2 — ê Hm wL The probability that a particle in this state is measured to be in the classically disallowed (c.d.) region is thus - —êHm wL pc.d. = KŸ -¶ = = = m w 1ê 2 I p— M 1 p 2 p +Ÿ ¶ —êHm wL - —êHm wL KŸ -¶ -1 ¶ O„x +Ÿ ¶ —êHm wL JŸ -¶ + Ÿ 1 N „ u ‰-u ¶ -u Ÿ1 „ u ‰ 2 J p í [email protected] - erfH1LD pc.d. = 1 - erf H1L y0 HxL 2 2 O„x‰ - u= m w x2 — ¬༼ Let „u...
View Full Document

Ask a homework question - tutors are online