(adsbygoogle = window.adsbygoogle || []).push({}); 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^{-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?

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# Quantum Mechanics: Choose an acceptable bound state function

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