- #1

Ryomega

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## Homework Statement

Particle of mass m in a 1D infinite square well is confined between 0 ≤ x ≤ a

Given that the normalised energy eigenfunction of the system is:

U

_{n}(x) = ([itex]\frac{2}{a}[/itex])

^{[itex]\frac{1}{2}[/itex]}sin ([itex]\frac{nx\pi}{a}[/itex])

where n = 1, 2, 3...

what are the corresponding energy levels?

## Homework Equations

Normalisation: 1 = [itex]\int[/itex] lψl

^{2}dx (from negative to positive infinity)

Energy Level for infinite well: E

_{n}= [itex]\frac{h^2}{2m}[/itex] ([itex]\frac{n}{2a}[/itex])

^{2}

Where h = reduced Planck constant (sorry couldn't find it)

## The Attempt at a Solution

At first I thought, I could just plug in 1, 2, 3 in U

_{n}(x)

But then I realized the question said that U

_{n}(x) is normalised.

Does this mean I have to reverse normalise U

_{n}(x)? If so, is this order right?

Make U

_{n}(x) = 1

Differentiate ([itex]\frac{2}{a}[/itex])

^{[itex]\frac{1}{2}[/itex]}sin ([itex]\frac{nx\pi}{a}[/itex])

Then square root whatever the result.

Am I going in the right direction or am I missing something out?

Thank you!