What is the correct method for solving the infinite square well energy problem?

[rsaad]

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.

 

[Bill_K]

You assumed the solution is of the form ψ = cos kx. There are also solutions of the form ψ = sin kx.

 

[rsaad]

yes, but as you see in the excerpt of the book, they have proved that the the given E holds for cos(kx) too

 

[rsaad]

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.

 

[rsaad]

If we were taking n>=0 then my solution was right.

 

[jtbell]

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.

 

[rsaad]

I do not understand what you said jtbell