Schrödinger Equation: Solving for Energy in a Semi-Infinite Square Well"

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The discussion revolves around solving the Schrödinger equation for a semi-infinite square well, highlighting the initial challenges faced in starting the problem. The user mentions the relationship between energy and wave number (K) and attempts to rearrange the equation to express energy (E) in terms of constants and variables. Key conditions at the boundary (X=L) are noted, specifically the requirement for first derivatives to match. The user seeks guidance on identifying the mass (m) and further solving the problem. The conversation emphasizes the complexities of applying quantum mechanics principles to a semi-infinite potential well scenario.
Ashley1nOnly
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Homework Statement


I have an attachment

Homework Equations


Schrödinger equation

The Attempt at a Solution


The issues I am having is how to start this one. This is not a infinite square well but a semi-infinite square well.
I know that energy= K^2= 2mE/h^2
Where h is planks constant 6.626 X 10^-34 J•s
So rearranging (K^2 • h^2)/(2m) =E
How do I find my m and solve the other ones

At X=L
The first derivatives must be equal at X=L
Asin(kL)=Ce^(-aL)
KAcos(kL)=-aCe^(-aL)

Am I going in the right direction
 
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I think this belongs in the advanced physics forum.
 

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