quantum mechanics

how to find probability from amplitude

what is a state

dynamical properties of a system

what is a ket

configuration of a system eg heads or tails

what is the first postulate

quantum system of a system is represented by a normalised vector with complex elements

what is a bra/dual

hermitian

what is an overlap/inner product

multiply vectors eg dot product

what is the relation between overlap conjugates

what makes an orthonormal basis

when states are normalised and mutually exclusive

what is postulate 2

when measuring a a system configuration in a basis that includes another configuration, the measurement outcome is the overlap mod squared, born rule

what is the sten-gerloch experiment

what are the rules of hermitian eigenvalues

eigenvalues are always real, hermitian matrices with different eigenvalues are orhtogonal

what are the properties of linear operators

what is indentity operator

leaves any quantum state unchanged

what is the average of a linear operator with respect to a state

what is the commutator for linear operators

what are useful relationships between commutators

what if commutator of A and B is 0

A and B share a complete set of eigenstates, have basis in which btoh A and B are measured at same time so are compatible

what is variance of an observable

what is the uncertainty principle

if you know 1 very well you do not know the other very well

what are hamiltonian operators

hermitian linear operators, associated with energy observables

what are the eigen properties of hamiltonian operators

eigenstates are states of well defined energy

eigen values are the discrete accessible energy levels

what is the time independent schrodinger equation

what is the time dependent schrodinger equation

what is postulate 3

time evolution of a closed quantum system is done by the schrodinger equation

what is the general solution of the schrodinger equation

what is ehrenfest’s theorem

time evolution of an observable A is

how to combine a system

what is equal to

what is equal to

what is equal to

what is not equal to

what is equal to

what is equal to

what is equal to

what is equal to

what is equal to

what is postulate 4

the state space of a composite physical system is the tensor product of the component physical system

what is entanglement

number of basis states in a composite system is the product of the number of constituents

eg can form equal tensor products out of states

what is the wave function

function of continuous variables

what is the probability of a wave function

what is the continuity equation

what is J

probabillity current