Can This Equation Be Applied to Both Continuous and Discrete Energy Spectra?

[M. next]

Is this equation only for continuous spectra?
they have used it to find the eigenvalues of energy spectra case of infinite potential well and we know that this case means discrete spectra..
can this equation in the attachment be used like in this case?

 

[cattlecattle]

Is this equation only for continuous spectra?
they have used it to find the eigenvalues of energy spectra case of infinite potential well and we know that this case means discrete spectra..
can this equation in the attachment be used like in this case?

Sigma should be used in place of integral sign for discrete spectra.

 

[M. next]

but check the attachment, he used it, check the question, and the solution.. i didnt include all questionsbut thr solution is an answer for the question.. find A so that psi(x,0) is normalized

 

[soothsayer]

Even if spectra are discrete, there's nothing wrong with integrating over the whole wavefunction in order to normalize, or find probabilities. The discreteness factors in when you realize that our expressions for $\psi$ and energy take on discrete values, usually separated by some integer factor n, but the wavefunctions themselves are continuous, so we can integrate over them.

 

[M. next]

ok thanks looooads,

 

[Jazzdude]

Sigma should be used in place of integral sign for discrete spectra.

Whether you're summing or integrating does not depend on the energy spectrum of a system but on the basis you chose for the operation. The result of an inner product is independent of the choice of the basis you expand the states into. If you expand into a discretely labeled basis (like a discrete energy basis or a spin basis) then you have to sum, if you expand into a continuously labeled basis (like a continuous energy spectrum or the momentum or position basis) then you have to integrate. The result is the same however.