- #1

Baynie

- 2

- 1

Hello everyone,

For weeks I have been struggling with this quantum mechanics homework involving writing a code to determine the energy spectrum and eigenvalues for the stationary Schrodinger equation for the harmonic oscillator. I can't find any resources anywhere. If anyone could help me get started, get my matrices and equations set up, or has worked a similar problem/written a similar code before, any help would be greatly appreciated! Thanks in advance!

Included in image above

Her is the code I have written so far. I'm not sure if this is even close or on the right track

% Stationary Schrodinger Equation - QHO

clear

clc

hbar = 6.58E-16;

f = 400E-9;

w = 2*pi*f;

m = 1;

N = 101;

a = 0.1;

n = 1:N;

r = n*a;

l = 1;

x = a;

mwhbar = m*w*hbar;

y = r;

% Operators (Matrices)

T = diag(-1*ones(1,N-2),2) + diag(2*ones(1,N-1),1) + diag(-1*ones(1,N),0);

K = (1/(2*a^2)) * T; % Kinetic Energy Matrix

Veff = -(1./r) + l*(l + 1)./(2*(r.^2));

V = diag(Veff);

U = (1/(2*a^2)) * V; % Potential Energy Matrix

% Equations

H = -(1/2*a^2)*(eigen_f(n+1) - 2 * eigen_f(n) * eigen_f(n-1));

For weeks I have been struggling with this quantum mechanics homework involving writing a code to determine the energy spectrum and eigenvalues for the stationary Schrodinger equation for the harmonic oscillator. I can't find any resources anywhere. If anyone could help me get started, get my matrices and equations set up, or has worked a similar problem/written a similar code before, any help would be greatly appreciated! Thanks in advance!

## Homework Statement

## Homework Equations

Included in image above

## The Attempt at a Solution

Her is the code I have written so far. I'm not sure if this is even close or on the right track

% Stationary Schrodinger Equation - QHO

clear

clc

hbar = 6.58E-16;

f = 400E-9;

w = 2*pi*f;

m = 1;

N = 101;

a = 0.1;

n = 1:N;

r = n*a;

l = 1;

x = a;

mwhbar = m*w*hbar;

y = r;

% Operators (Matrices)

T = diag(-1*ones(1,N-2),2) + diag(2*ones(1,N-1),1) + diag(-1*ones(1,N),0);

K = (1/(2*a^2)) * T; % Kinetic Energy Matrix

Veff = -(1./r) + l*(l + 1)./(2*(r.^2));

V = diag(Veff);

U = (1/(2*a^2)) * V; % Potential Energy Matrix

% Equations

H = -(1/2*a^2)*(eigen_f(n+1) - 2 * eigen_f(n) * eigen_f(n-1));