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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:
Un(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] lψl2 dx (from negative to positive infinity)
Energy Level for infinite well: En = [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 Un(x)
But then I realized the question said that Un(x) is normalised.
Does this mean I have to reverse normalise Un(x)? If so, is this order right?
Make Un(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!