- #1

Gatsby88

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## Homework Statement

Normalize the wave function

ψ(x,0) = C

^{1/4}* e

^{a(x2)-ikx}a and k are positive real constants

## Homework Equations

∫|ψ|

^{2}dx = 1

## The Attempt at a Solution

Now, my maths is a little weak, so I'm struggling a little bit here.

The constant is easy to deal with in all aspects of this problem, so that doesn't worry me, and I've ignored that below to make it easier to read.

When I'm squaring the e function, do I just square it or do I multiply by its complement?

If I use complements, the i bit goes away leaving e

^{-2ax2}.

If I square, I get e

^{-2ax2-2ikx}This can then be rewritten in the form of cos and sin which allows me to say that the sin function is odd so its integral is 0 and can be ignored (removing the imaginary part again), but it still leaves me with e

^{-2ax2}cos(2kx)

The question goes on to say that I should change the variable of integration and use a standard integral, and I can't see a standard integral looking like either of my avenues that I've pursued above.

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