- #1

alec_grunn

- 7

- 0

## Homework Statement

Ψ(x,0)=A(iexp(ikx)+2exp(−ikx)) is a wave function. A is a constant.

Can Ψ be normalised?

## Homework Equations

Code:

```
##
{\langle}p{\rangle}
= \Big( \sum_{n=1} \hbar C[SUB]n[/SUB] ^2) ##
```

Where C

_{n}

^{2}is the probability that the associated momentum will be observed.

## The Attempt at a Solution

My initial thought was, plane waves can't be normalised, since that would violate the normalisation condition.

But the equation above (from textbook 'foundations of modern physics'), implies one of two options in my mind. Either:

1) The wavefunction can be normalised by ## A= \frac{1}{\sqrt{5}} ##

2) The allowed momentum values are not ## p= ± \hbar k##, but ## p = ± \frac{\hbar k}{5A

^{2}}##

Both of these seem to have their own problems. The first because I've read in other places that plane waves can not be normalised (unless you have some a Fourier series which gives you a finite integral). And the second because the momentum should not vary due to its coefficient.

Cheers,

Alec