What forces the wavefunction to zero at the boundary of the infinite potential well? Is it the infinite height or the infinite width of the walls of the barrier or what?

I presume it's the infinite height, but in that case how do I interpret the fact that the delta function has a non zero coefficient of transmittance.

Even though the integral of the delta function equals one the height is still infinite isn't it?

Originally posted by Sacroiliac
What forces the wavefunction to zero at the boundary of the infinite potential well? Is it the infinite height or the infinite width of the walls of the barrier or what?
i guess it is the infinite height, along with the nonzero width (anticipating your question)

I presume it's the infinite height, but in that case how do I interpret the fact that the delta function has a non zero coefficient of transmittance.

i would say that it is not as simple as saying "the height is infinite, therefore the wavefunction must be zero". you have to consider what kind of wavefunctions are allowed in each region of the potential, and see if you can make them continuous.

the finite width infinite height potential allows only a 0 wavefunction in its interior. so that is your only choice. on the other hand, the delta function potential doesn t have a finite width. it is really just a point discontinuity, so i cannot say concretely that the wavefunction must be zero within its interior. in fact, it doesn t have an interior, it is zero almost everywhere!

how about a more physical way to think of this: lets take a finite height, finite width potential wall. let the area of this wall be 1. then for any width, there will always be a finite transmission probability. now take the limit as this width goes to zero, and you still have a finite transmission probability.

Even though the integral of the delta function equals one the height is still infinite isn't it?
yeah, the height is infinite. but it is also infinitely narrow, and i think that is important here.

so, i guess you re still working through griffiths, eh? are you doing this for a class?

You're good lethe. No doubt about it.

so, i guess you re still working through griffiths, eh? are you doing this for a class?

No, I'm a businessman who studies this stuff, the few chances I get, just because I find it fascinating. So I really appreciate your help as there's no where else I can get my questions answered.

yeah, the height is infinite. but it is also infinitely narrow, and i think that is important here.

What's really weird is that the damn thing supports a bound state. And if you take a look at problem 2.26 it gets even weirder. A double delta function well supports one bound state for an alpha value of h^2/4ma, and two bound states for an alpha of h^2/ma. And yet regardless of alpha they're both supposedly infinitely high and infinitely narrow. Too much for my pea brain.

Originally posted by Sacroiliac

No, I'm a businessman who studies this stuff, the few chances I get, just because I find it fascinating. So I really appreciate your help as there's no where else I can get my questions answered.

as i suspected. well let me say i think you re making excellent progress. and you couldn t have chosen a better book for self-study.

it will get a little harder, but stick with it.

What's really weird is that the damn thing supports a bound state. And if you take a look at problem 2.26 it gets even weirder. A double delta function well supports one bound state for an alpha value of h^2/4ma, and two bound states for an alpha of h^2/ma. And yet regardless of alpha they're both supposedly infinitely high and infinitely narrow. Too much for my pea brain.

yes, i also thought it was quite weird when i learned that the delta function has a bound state. luckily, this potential is totally unphysical. you will see in the next section, though, that a well always has one bound state, no matter how shallow or deep it is.

as for the double bound state, well you should expect there to be something funny happening for the right seperation. the size of the delta function determines the energy scale, which also sets a natural scale for oscillations. when these match up, you can find more states. i sort of imagine this like the finite barrier. when the energy of the particle matchs the width of the barrier, funny things can happen like the reflection coefficient vanishes.