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%                       Computational Physics
%                             FALL 2008
%
%                     Instructor: Kevin H. Knuth
%
%
% HW 2
% Particle in a Quantum 1-D Finite Well
%
% This is our first application in which we will solve a physics problem
% numerically.  Consider a particle of mass m in a finite well of width L
% and barrier potential Vo.  In your report solve Schroedinger's equation
% for this problem and derive the two equations that must be solved to find
% the energy levels.  These are:
% even solns: k tan(k L/2) = a
% odd solns:  -1/k tan (k L/2) = 1/a
% where a = sqrt(b^2 - k^2), k = sqrt(2mE/hbar^2), b = sqrt(2mVo/hbar^2)
% * Use MKS units for masses and lengths, and eV for energies.
%
% plotSOLNS.m
% Write a function that takes m, L and Vo as arguments, and plots the three
% functions a/k (black), tan(kL/2) (blue), -cot(kL/2) (red) as a function 
% of energy ranging from a sufficiently small energy to Vo.  
% Be aware of the scale of the problem, and the fact that a/k goes to 
% infinity at E = 0.
%
%       USAGE:
%       h = plotSOLNS(m, L, Vo)
%
%       INPUT:
%       m - mass of the particle (in kg)
%       L - width of the box (in m)
%       Vo - potential of the walls (in eV)
%   
%       OUTPUT:
%       h - figure handle
%
% energyLEVELS.m
% Write a function that takes m and Vo and computes the energy levels.
%
%       USAGE:
%       E = energyLEVELS(m, L, Vo)
%
%       INPUT:
%       m - mass of the particle (in kg)
%       L - width of the box (in m)
%       Vo - potential of the walls (in eV)
%   
%       OUTPUT:
%       E - 1xn array of energy level values (in eV)
%
%
% plotWAVEFNS.m
% Combine these results in a function that takes m and Vo and plots a
% potential well, with the wavefunctions separated in height by their
% energy.  Be sure to include both the sinusoidal and exponential parts!
%
%       USAGE:
%       h = plotWAVEFNS(m, L, Vo)
%
%       INPUT:
%       m - mass of the particle (in kg)
%       L - width of the box (in m)
%       Vo - potential of the walls (in eV)
%   
%       OUTPUT:
%       h - figure handle
%
% Test these functions on an electron in a 75eV deep well 0.4 nm across.
%
% TURN IN:
% Three m-files titled: plotSOLNS.m, energyLEVELS.m, plotWAVEFNS.m
% along with report which includes derivations, plots from plotSOLNS,
% plotWAVEFNS for an electron an electron in a 75eV deep well 0.4 nm across.
%
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% Problem by: Kevin H. Knuth
% Created on: 18 January 2008
%
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