(adsbygoogle = window.adsbygoogle || []).push({}); I'm working on an assignment where I'm required to numerically find the energy of a delta-potential's bound state. To do this, we've converted the time-independent schrödinger equation to an eigenvalue problem with E the eigen value, ψ the eigen vector and H a matrix as follows:

with ##t = \frac{\hbar^2}{2ma^2}##.

Now, my specific problem is this:

I've already done all the theoretical calculations, and am just left with figuring out the code. I've tried a bunch of things, but I haven't been able to get the bound state to appear. My code is as follows:

I'm quite desperate, hence the post here. Thanks in advance for all your help!Code (Python):import numpy as np

import matplotlib

matplotlib.use("TkAgg")

import matplotlib.pyplot as plt

#################################################

# Parameter input

#################################################

hbar = 1.05e-34

h = 6.626e-34

m = 1

N = 400

a = 1

L = N * a

t = hbar**2 / ( 2 * m * a**2)

#################################################

# Parameter sanity check

#################################################

assert N%2 == 0, 'N must be an even number'

assert m > 0, 'Mass must be positive'

assert a > 0, 'Distance between points must be positive'

assert t >= 0, 'T must be non-negative. Make sure hbar is positive.'

#################################################

# Base code

#################################################

for i in range(0,100,10):

# Building the hamiltonian operator matrix and calculating its eigen

# values (eval) and eigen vectors (evec)

n = int(N/2)

a1 = np.full((N-1,), -t)

a2 = np.full((N,), 2*t)

Hamiltonian = np.diag(a1, -1) + np.diag(a2) + np.diag(a1, 1)

Hamiltonian[n,n] = Hamiltonian[n,n]- 1*10**i # Adds potential in middle.

eval, evec = np.linalg.eigh(Hamiltonian) # use .eig() if Hamiltonian is not symmetric

plt.plot(evec)

plt.show()

For those amongst you who'd prefer a nicely formatted image of the assignment: https://puu.sh/yKp4D/b668471918.png

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# Homework Help: Numerically find the energy of the delta-well's bound state

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