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 Exercise [21.05] 
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Joined: 26 Mar 2010, 04:39
Posts: 109
Post Exercise [21.05]
To find a solution of the Schrodinger equation with a gravitational potential, I first got a solution to the equation with V=0 using separation of variables and then transformed it to a solution of the equation with V=mgz using the result from exercise 21.6.


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27 Jul 2010, 04:09

Joined: 26 Mar 2010, 04:39
Posts: 109
Post Re: Exercise [21.05]
I just updated the file with minor corrections.


28 Jul 2010, 03:45

Joined: 12 Jul 2010, 07:44
Posts: 154
Post Re: Exercise [21.05]
The k=0 case is not unphysical. On the contrary, it is a momentum eigenstate, for a stationary particle with exactly zero momentum, zero energy!

Also, I believe you've made a numerical error somewhere, because the t^3 term in the final answer should be -\frac{i m g^2 t^3}{6 \hbar} not -\frac{i m g^2 t^3}{3 \hbar} ... i.e. you need a 6 rather than a 3 in the denominator. (Verified by my own calculations, and also Roberto's posted solution).


12 Aug 2012, 20:22
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