2. QM Background

Question 1

Postulate 1 of QM

Answer 1

The state of a system is fully described by ψ, a mathematical function of the system. This must be finite, continuous and single valued.

Question 2

Postulate 2 of QM

Answer 2

Every dynamical variable (observable) is represented by a corresponding linear, Hermitian operator.

Question 3

Postulate 3 of QM

Answer 3

When a dynamical variable A is measured, there are only certain possible values that may be obtained. These values are the eigenvalues a of the operator ˆA given by ˆAψ=aψ. Here ψ is an eigenfunction of the operator ˆA that represents the dynamical variable A.

Question 4

Postulate 4 of QM

Answer 4

The wavefunction for the state of a system is provided as a solution of the equation
^Hψ = Eψ
Where ^H is the Hamiltonian operator for the total energy of the system.

Question 5

Probability Density

Answer 5

|ψ|^2 is the probability density
ψ is the probability amplitude
ψ can be positive, negative or imaginary but |ψ|^2 is always positive and real
|ψ|^2 = ψψ where ψ is the complex conjugate