Exact Solution to the double well potential problem in mathematica

• To: mathgroup at smc.vnet.net
• Subject: [mg132438] Exact Solution to the double well potential problem in mathematica
• From: Ragavendran Nagarajan <ragavendran.nagarajan at gmail.com>
• Date: Sat, 15 Mar 2014 03:47:05 -0400 (EDT)
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```A little background. This is a Schrodinger equation problem to find the energy stages e in the double well where there is a step potential inside a infinite rectangular well. After solving the boundary conditions analytically, I tried to solve the following program in mathematica

hbar := 1.05*10^-34;
m := 0.096*9.11*10^-31;
a := 5*10^-9;
b := 0.5*10^-9;
V := 0.3*1.6*10^-19;
k = Sqrt[(2*m*e)/((hbar)^2)];
l = Sqrt[(2*m*(V - e))/(hbar)^2];
Block[{e}, e /. First@Solve[k*Cot[(-k)*a] - l*Tanh[(-l)*b/2] == 0, e]]

As you can see since the values of the constants are very small, I am getting a lot of errors and I am not sure how to get the solution.

Please let me know if there is a way to solve this equation using Mathematica. I have to submit this assignment in a couple of days, so I wold be really really grateful if you guys can show me the way to solve this.