- #1

511mev

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**1. Which of the following is an allowed wave function for a particle in a bound state? N is**

a constant and α, β>0.

1) Ψ=N e

2) Ψ=N(1-e

3) Ψ=Ne

4) Ψ=Non-zero constant if r<R , Ψ=0 if r>R

Only one is correct.

a constant and α, β>0.

1) Ψ=N e

^{-α r}2) Ψ=N(1-e

^{-α r})3) Ψ=Ne

^{-α x}e^{-β(x2+y2+z2)}4) Ψ=Non-zero constant if r<R , Ψ=0 if r>R

Only one is correct.

**2. What are the criteria for acceptable bound state wave functions?**

**3. I did assume that one of the criteria is that the wave function must go to zero at infinity. To show this, I took the limits as r goes to infinity and, for the function given in 3, as x,y,z, go to positive and negative infinty. I got that all are zero at infinity except 2.**

Another requirement is that the function be smooth and continuous. Since 4 has an abrupt change, i.e., its derivative is infinite at R, then it is not smooth.

That leaves 1 and 3. What additional property am I forgetting?

Another requirement is that the function be smooth and continuous. Since 4 has an abrupt change, i.e., its derivative is infinite at R, then it is not smooth.

That leaves 1 and 3. What additional property am I forgetting?