Question

(b) Consider a particle of mass $m$ moving freely between $x = 0$ and $x = a$ inside an infinite square well potential. Calculate the expectation values $\langle x \rangle_n$, $\langle p \rangle_n$, $\langle x^2 \rangle_n$ and $\langle p^2 \rangle_n$, and compare them with their classical counterparts. (c) Derive the degeneracy of a harmonic oscillator $g_n = \frac{1}{2}(n+1)(n+2)$.

Name: b consider a particle of mass m moving freely between x 0 and x a inside an infinite square well potential calculate the expectation values langle x ranglen langle p ranglen langle x2 rang 80885
Uploaded: 2023-06-13T14:05:06-08:00
Duration: 3 min 50 s
Channel: Madhur L
Description: b consider a particle of mass m moving freely between x 0 and x a inside an infinite square well potential calculate the expectation values langle x ranglen langle p ranglen langle x2 rang 80885

          (b) Consider a particle of mass $m$ moving freely between $x = 0$ and $x = a$ inside an infinite square well potential. Calculate the expectation values $\langle x \rangle_n$, $\langle p \rangle_n$, $\langle x^2 \rangle_n$ and $\langle p^2 \rangle_n$, and compare them with their classical counterparts.

(c) Derive the degeneracy of a harmonic oscillator $g_n = \frac{1}{2}(n+1)(n+2)$.

b consider a particle of mass m moving freely between x 0 and x a inside an infinite square well potential calculate the expectation values langle x ranglen langle p ranglen langle x2 rang 80885

Added by Martin W.

University Physics with Modern Physics

Hugh D. Young 14th Edition

Instant Answer

Solved by Expert Madhur L

06/13/2023

Step 1

The wavefunctions for this system are given by: $\psi_n(x) = \sqrt{\frac{2}{a}}\sin(\frac{n\pi x}{a})$ for $0 \le x \le a$ and 0 otherwise. where $n = 1, 2, 3, ...$ Show more…

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(b) Consider a particle of mass $m$ moving freely between $x = 0$ and $x = a$ inside an infinite square well potential. Calculate the expectation values $\langle x \rangle_n$, $\langle p \rangle_n$, $\langle x^2 \rangle_n$ and $\langle p^2 \rangle_n$, and compare them with their classical counterparts. (c) Derive the degeneracy of a harmonic oscillator $g_n = \frac{1}{2}(n+1)(n+2)$.