(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

problem 1.4 of Cohen Tannoudji:

The exercise is divided into two parts:

THE FIRST ONE (part a.) asks to find the Fourier transform of a wave function when the potential is: -αδ(x). In terms of p, E, alpha and ψ(0)

and

ask to “show that only one value of E, a negative one, is possible” Furthermore, they claim that “Only the bound state of the particle, and not the ones in which it propagates, is found by this method; why?”

2. Relevant equations

the Schrodinger equation:

-ℏ^2/2m d^2/〖dx〗^2 ψ(x)-αδ(x)ψ(x)=E ψ(x)

3. The attempt at a solution

Hi, I was solving the problem 1.4 of Cohen Tannoudji:

The exercise is divided into two parts:

THE FIRST ONE (part a.) asks to find the Fourier transform of a wave function when the potential is: -αδ(x). In terms of p, E, alpha and ψ(0)

I did the next procedure:

I wrote down the Schrodinger equation:

-ℏ^2/2m d^2/〖dx〗^2 ψ(x)-αδ(x)ψ(x)=E ψ(x) …………………………………………………………………… (i)

Then, I applied a Fourier Transform over the equation (i) What I got was:

-ℏ^2/2m 〖(ik)〗^2 ψ ̅(k)-αψ(0)=E ψ ̅(k)………………………………………………………………………….(ii)

Finally, I express ψ ̅(k) in terms of the given parameters, using the fact that p=ℏk

ψ ̅(k)=(α ψ(0))/(p^2/2m-E)…………………………………………………………………………………………………………(iii)

Now, they ask to “show that only one value of E, a negative one, is possible” Furthermore, they claim that “Only the bound state of the particle, and not the ones in which it propagates, is found by this method; why?”

What I know is that as E=V(r)+p^2/2m and for x≠0 V(r)=0, then equation (iii) diverge. But, I don’t get why there’s

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Homework Help: Chapter 1 cohen tannoudji

**Physics Forums | Science Articles, Homework Help, Discussion**