Quantum Particle in a Box / Infinite Potential Well / Infinite Square Well (One-Dimensional Case) 

When determining the normalization constant A, the positive real root was considered. This is because the phase of A has no physical significance.

I got confused when I tried to verify the normalisation constant, and I see that someone else in the comments was also confused by the same thing, so I'll post the steps that I eventually worked out in case this helps to clear the confusion for anyone else ! So, we want to normalise the wavefunction, psi(a) = Asin(ka) Take the square of the magnitude of the wavefunction to get the integrand, A^(2)sin^(2)(ka), and integrate it with respect to " a " with bounds of " a " to 0 The result of this integral is (A^(2)ka - 0.5*A^(2)sin(2ka)) / 2k + C C is absorbed into the constant k So, we get (A^(2)ka - 0.5*A^(2)sin(2ka)) / 2k We have found the value of k, defined as " k_n=((n)(pi)) / a " for which k satisfies the continuity boundary of the wavefunction. Substitute k_n into every k term in the result of the integral This gives ((A^(2)(n)(pi) - A^(2)sin(2(n)(pi)))a) / 2(n)(pi) The second term of the nominator is equal to 0 because n is any natural number so sin(2(n)(pi))=0 Now we have (A^(2)(n)(pi)) / 2(n)(pi), which we want to be equal to 1 to satisfy the normalisation condition Rearrange (A^(2)(n)(pi)) / 2(n)(pi) = 1 and solve for A This gives sqrt(2/a) And, as Elucyda said, "When determining the normalization constant A, the positive real root was considered. This is because the phase of A has no physical significance."

Miller Helen Jackson John Gonzalez Ronald

Amazing ❤

Great video - thanks, you explain things really clearly ... in my text book it talks about a particle in a box with standing waves as an analogy to an electron in an atom what I don't get is that here we get E proportional to n^2 whereas energy levels in an atom converge because E is proportional to 1/n^2 so this suggests particle in a box is not a good way to think of schrodinger's atomic energy levels. Is there any way that this approach could be modified so it works?

Great video series really helping with my Quantum module! Thankyou so much!

Thank you for your great explanation

This is really awesome!! Thank you for explaining each step thoroughly, it makes it so much easier to understand! I still don't understand the normalization constant though, sqrt(2/a)