A ket vector describes the state of a quantum system.

A bra vector describes the state of a quantum system.

An operator describes an observable (a Hermitian operator) or an action (a unitary operator).

State of a spin-1/2 particle if measurement in the x-direction would give angular momentum +hbar/2.

State of a spin-1/2 particle if measurement in the x-direction would give angular momentum -hbar/2.

State of a spin-1/2 particle if measurement in the y-direction would give angular momentum +hbar/2.

State of a spin-1/2 particle if measurement in the y-direction would give angular momentum -hbar/2.

State of a spin-1/2 particle if measurement in the z-direction would give angular momentum +hbar/2.

State of a spin-1/2 particle if measurement in the z-direction would give angular momentum -hbar/2.

State of a spin-1/2 particle if measurement in the n-direction, described by spherical polar angle theta and azimuthal angle phi, would give angular momentum +hbar/2.

State of a spin-1/2 particle if measurement in the n-direction, described by spherical polar angle theta and azimuthal angle phi, would give angular momentum -hbar/2.

The Pauli X operator.

The Pauli Y operator.

The Pauli Z operator.

Pauli operator for an arbitrary direction given by spherical coordinates theta and phi.

Alternative definition of Pauli operator for an arbitrary direction.

Given a time step and a Hamiltonian operator, produce a unitary time evolution operator. Unless you really need the time evolution operator, it is better to use timeEv, which gives the same numerical results without doing an explicit matrix inversion. The function assumes hbar = 1.

Given a time step and a Hamiltonian operator, advance the state ket using the Schrodinger equation. This method should be faster than using timeEvOp since it solves a linear system rather than calculating an inverse matrix. The function assumes hbar = 1.

The possible outcomes of a measurement of an observable. These are the eigenvalues of the operator of the observable.

Given an obervable, return a list of pairs of possible outcomes and projectors for each outcome.

Given an observable and a state ket, return a list of pairs of possible outcomes and probabilites for each outcome.

Generic multiplication including inner product, outer product, operator product, and whatever else makes sense. No conjugation takes place in this operation.

The adjoint operation on complex numbers, kets, bras, and operators.

An orthonormal basis of kets.

Make an orthonormal basis from a list of linearly independent kets.

The orthonormal basis composed of xp and xm.

The orthonormal basis composed of yp and ym.

The orthonormal basis composed of zp and zm.

Given spherical polar angle theta and azimuthal angle phi, the orthonormal basis composed of np theta phi and nm theta phi.