# 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.

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