Infinite square well energy

  • Thread starter rsaad
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  • #1
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Hi

I have attached my attempt of solving the infinite square well for Energy. The value I get is different from that of the book, also in the attachment,
Kindly explain if my answer is correct given the fact that I proceeded step by step and used no tricks.
Thank you.
 

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  • #2
Bill_K
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You assumed the solution is of the form ψ = cos kx. There are also solutions of the form ψ = sin kx.
 
  • #3
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yes, but as you see in the excerpt of the book, they have proved that the the given E holds for cos(kx) too
 
  • #4
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I think my solution wrong because I have taken k*a/2 = (n+ 0.5)*pi
For the given situation, for x=a/2 for cos((n+ 0.5)*pi*x)=0 is only possible if n=0, but we are taking n>0.
 
  • #5
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If we were taking n>=0 then my solution was right.
 
  • #6
jtbell
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The sine and cosine solutions should alternate with n. The ground state is a cosine, the next higher state is a sine, the next one is a cosine, etc.

If you put the walls of the box at x = 0 and x = a, it's easier because all the solutions are sines.
 
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  • #7
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I do not understand what you said jtbell
 

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