Answer to Question #189029 in Quantum Mechanics for yash

Question #189029

A particle trapped in a one-dimensional box of length L is described by the wave function ψ = ax. What is the probability that the particle is lying between L1 and L2?


1
Expert's answer
2021-05-05T10:55:18-0400

By definition, the probability that the particle is lying between L1 and L2 is given as follows (see http://www.iitg.ac.in/asil/QM-02.pdf):


"P = \\int_{L_1}^{L_2}|\\psi|^2dx"

where


"|\\psi|^2 = (ax)^2 =a^2x^2"

is the modulus of the wavefunction. Thus, evaluating the integral, obtain:


"P = a^2\\int_{L_1}^{L_2}x^2dx = a^2\\left.\\dfrac{x^3}{3}\\right |_{L_1}^{L_2} = \\dfrac{a^2}{3}(L_2^3-L_1^3)"

Answer. "P = \\dfrac{a^2}{3}(L_2^3-L_1^3)".


Need a fast expert's response?

Submit order

and get a quick answer at the best price

for any assignment or question with DETAILED EXPLANATIONS!

Comments

No comments. Be the first!

Leave a comment

LATEST TUTORIALS
New on Blog
APPROVED BY CLIENTS