- #1

- 3

- 0

ψ

_{n}(x) = A * √x * sin (n∏x

^{2}/L

^{2}), n = 1, 2, 3, ...

Normalized in the range 0 to L.

Thanks for the help, a little bit of a walk through would be much appreciated.

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- Thread starter theblender
- Start date

- #1

- 3

- 0

ψ

Normalized in the range 0 to L.

Thanks for the help, a little bit of a walk through would be much appreciated.

- #2

jtbell

Mentor

- 15,866

- 4,449

What have you tried so far, and where are you stuck?

- #3

- 3

- 0

- #4

- 3

- 0

Also having trouble integrating the statement cos ((2*pi*x^2)/L^2) dx.

- #5

- 127

- 0

Also having trouble integrating the statement cos ((2*pi*x^2)/L^2) dx.

Hint: you need to substitute x for some variable y so that you end up with cos(y^2) in the integrand. Then you can try messing around with trig, for example cos(y^2) = cos(y*y) = ?

You realize there is no easy way to expand that. In fact, wolframalpha gives:

http://www.wolframalpha.com/input/?i=cos(x^2)

which uses the "Fresnel C Integral" which I haven't even come across until this example.

So the integral is not representable by standard elementary functions...

Edit: However integrating the square of your original wavefunction is quite straightforward once you calculate the integral of x(sin^2)(x^2).

Use the fact that (sin^2)(y) = (1/2)(1-cos(y))

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