The first
part of this website on quantum mechanics arose from reading the book
"Quantum Mechanics: The Theoretical Minimum" by Leonard Susskind. It
covers the basics of quantum mechanics up to the harmonic oscillator, including
the math necessary.
Susskind's
website is at https://theoreticalminimum.com/
A dictionary of quantum mechanics at beginners’
level you find here: quantumabc.
The second part of this website deals with the
basics of quantum computing. It is under construction and constantly being
updated.
…errors, broken links? … please give me a hint
...
You can reach me via the emailaddress dieter.kriesell (at) gmx.de
Dieter Kriesell
Quantum
mechanics:
The 2Dharmonic
oscillator in cartesian and polar coordinates. 

We calculate angular
momentum in spherical coordinates both classic and quantum. 

Two examples for the
chain rule for partial derivatives. 

Two observables are
simultaneously measurable if and only if the respective matrices commutate. 

How to calculate
commutators that contain a function of one operator. 

Solving integrals
containing sin and cos by use of complex functions. 

This paper describes
how a continuous function can be quantized and how differentiation and
integration are expressed explicitly with matrices. 

We solve
differential equations of first and second order with emphasis to complex
solutions. 

The Dirac function and the position operator . 

This paper shows the
transformation process from discrete probability to continuous probability
density. It is a kind of reverse process compared with the paper above. 

A translation of the
original paper with some comments. 

From classical
physics to quantum mechanics via the Ehrenfest
Theorem. 

Power series of
exponentials containing Pauli matrices. 

How to handle
exponentials with Pauli matrices. 

How to
solve the timedependent Schrödinger equation (no potential). Show that there
exist solutions representing plane waves and discuss their physical meaning. 

How to
solve a wave packet in one dimension without potential by superposition of
plane waves. 

We have a
particle in a 3Dbox. Within the box we have potential zero and infinity
outside. How to calculate the energy eigenvalues and the eigenfunctions. 

How to Calculate
energy values and eigenfunctions for the onedimensional potential well. 

How to
calculate energy values and eigenfunctions for the onedimensional undamped
harmonic oscillator. 

The free particle
and its wave function. 

Basics for
understanding Fourier series 

Proofs for some
Gauss Integrals. 

An example that
shows that a 2x2 Hermitian matrix can be transformed in diagonal form. 

We become acquainted
with Hermite polynomials and proof orthogonality. 

This paper starts
with a finite dimensional Hilbert space and ends up with the spin of an
electron. 

We check the
derivation rules with cartesian and polar coordinates. 

This short paper
describes the Lorentz transformation in the simple case two systems moving
away from each other at constant speed on the xaxis. 

This is more or less
an exercise in complex arithmetic. 

A compilation of
mathematics you need if you want to start with quantum mechanics. 

Two ways to write a
matrix in a new basis. 

States with position
and momentum will be described with either position wave functions or
momentum wave functions. This paper presents both descriptions parallel. 

Uncertainty of
momentum and position Operator in momentum and position representation. 

We take a close look
at the harmonic oscillator and number operator, raising operator and lowering
operator. 

An illustration of
the spin problem and the tensor product. 

Partial derivatives
in cartesian and polar representation. 

We work with the 1D
step barrier problem and use the probability current to develop reflection
and transmission probability 

Time development and
Schroedinger equation for constant and commutating
time dependent Hamiltonians. 

Here you find a
compilation of keywords for quantum mechanics on a basic level. 

These are the
exercises of the book “Quantum Mechanics, The Theoretical Minimum” of Leonard
Susskind & Art Friedman. 

A traditional access
to the quantum mechanic oscillator and the Hermite polynomials. 

We calculate the
ratio of incoming to outgoing wave. 

Timeindependent vs.
timedependent operators. 

Two ways to get
timedependent Heisenberg operators out of timeindependent Schroedinger operators. 

We look at a spin ½
in a magnetic field: 
constant in direction and strength, 
constant in direction but slowly changing its strength, 
rotating (NMR). 

We substitute the variable
in a polynomial and an exponential function and take a look at the
derivatives. 

Tensor products,
correlation, and superposition. 

The trigonometric
identities resolved in exponential terms. 

We start from
classic physics, use de Broglie and arrive at the Schroedinger
equation. 

The infinite
potential well is either presented by use of trigonometric or complex
exponential functions. This paper works simultaneously through both and shows
the difference – in the end all works fine. 

Unitarian matrices
don’t change the dot product, map orthonormal bases to orthonormal bases and
play an important role in the time development of quantum states. 

We calculate the
speed of the electron of the hydrogen atom by use of the quantum mechanical
Viral theorem. 

Wave functions
(normalized polynomials) and matrices. 
Quantum
computing:
Four Bell states in
detail. 

The quantum Fourier
transformation explicit for 1, 2, 3 and 4 qubits. 

Application of
Simon’s problem to a fourbit and a twobit function, more mathematical. 

Practical
application of Simon’s problem from a programmer’s point of view. 

An alternative
access to the DeutschJozsa algorithm for a 3qubit input. 

An explicit and
detailed workthrough the Deutsch algorithm. 

This is a detailed
example of applicating Grover’s algorithm to a SAT problem. 

List of combinations
of 0>, 1>, +>, >, y+>, y> states with the Kroneckerproduct (tensorproduct). 

Arithmetic with bras
and kets of different dimension 

A short description
of spin states, the Hadamard Matrix, Bloch sphere and rotation. 

The Toffoli and the Fredkin quantum gates. 

We examine a quantum
circuit on conceptual level and basic level. 

We construct the
CNOTgate and its inverse. 

We work through a
qubitexercise, measuring Bellstates on both conceptual and basic level. 

We work through an
example of quantum teleportation on both conceptual and basic level. 
Last
actualization July 2024