Quantum Mechanics Library

A small python quantum mechanics library which simplifies the notation of numpy and tailors it for quantum mechanics teaching

Installation

The library can be used by placing the QM.py alongside your code, or be installed on your system by typing the following into your terminal:

python setup.py install

The library is also registred with PyPi and you can install it with:

pip install QM-KU==1.1.1

Quick start

# Load library
import QM as q

# bra <v| = [1, 5, 2]
v = q.bra([1, 5, 2])

# ket |w> = [9, 0, 5]
w = q.ket([9, 0, 5])

# Operator M = [7, 3, 0]
#              |2, 7, 3|
#              [8, 4, 5]
M = q.operator([[7, 3, 0], [2, 7, 3], [8, 4, 5]])

# <v|w>
a = v * w

# <v|v*>
b = v * v.H

# <v|M|w>
c = v * M * w

Documentation

This library introduces three classes bra, ket and operator.

All of three objects are array-like: bra, ket are vector-like, while operator is matrix-like.

The classes are subclasses of numpy.ndarray, and they work with numpy functions. (e.g. np.shape(), np.linalg.norm())

The classes overload the arithmatic operators +, -, and * such that they obey the rules of Dirac notation. That is, multiplication can only be done between the correct classes and the operations do not commute.

In addition to introducing Dirac-like arithmatic operator, the library includes two methods:

.prob() - Which works on bra and ket and returns a numpy.ndarray containing the absolute value of each element

.eig() - Which works on operator and returns a tuple containing a numpy.ndarray of sorted eigenvalues, followed by an operator with the sorted eigenvectors. The n'th eigenvector is stored at index n in the operator.