Register to reply

Normalizing wave function

by SoggyBottoms
Tags: function, normalizing, wave
Share this thread:
Mar12-12, 03:45 PM
P: 61
At t = 0 a particle is in the (normalized) state:

[tex]\Psi(x, 0) = B \sin(\frac{\pi}{2a}x)\cos(\frac{7\pi}{2a}x)[/tex]

With [itex]B = \sqrt{\frac{2}{a}}[/itex]. Show that this can be rewritten in the form [itex] \Psi(x, 0) = c \psi_3(x) + d \psi_4(x)[/itex]

We can rewrite this to:

[tex]\Psi(x, 0) = \frac{B}{2}\left[ c \sin(\frac{4 \pi}{a}x) - d\sin(\frac{3\pi}{a}x)\right][/tex]

The answer sheet gives [itex]c = -d = \frac{1}{\sqrt{2}}[/itex]. I assume you can find this by calculating [itex]A^2 \int \left[ c \sin(\frac{4 \pi}{a}x) - d\sin(\frac{3\pi}{a}x)\right]^2 dx[/itex]. I attempted to do it this way, but it becomes a really long calculation and halfway through I just lose track of everything. Is there an easier way to find c and d?
Phys.Org News Partner Physics news on
Step lightly: All-optical transistor triggered by single photon promises advances in quantum applications
The unifying framework of symmetry reveals properties of a broad range of physical systems
What time is it in the universe?
Mar12-12, 07:54 PM
Sci Advisor
HW Helper
PF Gold
P: 2,602
The difference between the two expressions is just a trig identity that you should be able to work out with no unknown coefficients. Therefore, if you can verify that B is the correct normalization factor for the first version, c and d are just determined by the trig identity.

However, if you are going to be studying QM, you should really learn how to do integrals like the one that gave you trouble. That is fairly simple compared to integrals you will come across later. QM is not a forgiving subject if you don't have a good calculus background.

Register to reply

Related Discussions
Normalizing a wave function, what does it mean? Quantum Physics 14
Normalizing Wave Function of A Ring Advanced Physics Homework 6
QM: Normalizing a wave function Advanced Physics Homework 5
Particle in a Box, normalizing wave function Advanced Physics Homework 2