# Imaginary Normalisation Constant

1. Homework Statement

A one-dimensional system is in a state at time t=0 represented by:

Q(x) = C { (1.6^0.5)Q1(x) - (2.4^0.5)Q2(x)}

Where Qn(x) are normalised eergy eigenfunctions corresponding to different energy eigenvalues, En(n=1,2)

Obtain the normalisation constant C

3. The Attempt at a Solution

I get C= i(1.2)^0.5 from the following equation:

C^2 * (1.6 (int( Q1 ^2 dx) - 2.4(int ( Q2 ^2 dx = 1

So C^2 has to be -5/4 in order for the above to be true. Is this right?
Just a bit confused over whether it's possible to have an imaginary value for the normalisation constant? Thanks for any help you can give.

## Answers and Replies

Related Advanced Physics Homework Help News on Phys.org
You havent formed the product Q(x)Q*(x) correctly. What is special about energy eigenstates?

they follow linear superposition? so the integral of the total wavefunction squared is equal to the integral of 1.6*Q1^2 plus the integral of 2.4*Q2^2?

dextercioby
Homework Helper
What is Q* equal to ? How do you define the scalar product?

Daniel.

Well there aren't any imaginary parts to the first wavefunction since its just in the form Q = C ( XQ1 - YQ2) so Q* is just the same as Q.

Gokul43201
Staff Emeritus