# Homework Help: Solving transcendental equation- Quantum Mechanics

1. Feb 23, 2006

### GTdan

I don't know if I am being dumb or not but I need to solve a transcendental equation numerically and I need to write a program that can do this. The equation is so I can find the the ground state energy of a wave function in a semi-infinite well. I was told to use the Newton-Raphson method to do it and I am thinking of a transcendental equation found in the book would be the one I need to solve (if anyone thinks differently let me know). Here is the equation:

tan(z)=sqrt((z(o)/z)^2-1)

where z(o)=(a/h)*sqrt(2mV(o))

z=(a/h)*sqrt(2m(E+V(o)))

and V(o)= -10 eV

This is written in maple code btw. I'm thinking I can solve for z by using Newton's method and then solve for E afterwards since z is a function of E. That's the only idea I have that I would need Newton's method to do so can someone let me know if I am on the right track or give me some hints or something.

2. Feb 23, 2006

### arildno

Okay, so you're basically after a programming procedure, since you've already decided upon using Newton-Raphson?

3. Feb 23, 2006

### GTdan

Well, we have to use Newton Raphson. I would much rather solve it graphically like the book but that's not the case. I may have been vague but my problem is that I am I have no idea if I am going the right direction or not. Am I using the right equation to solve for E? If I am can I get some hints on the programming procedure?

Also, unless I can make Maple compile a program or something (if it even does that), I have to write it in C++.