Semester 1: Questions

Question 1

What is meant by a quantum state?

Answer 1

The state of a non-relativistic quantum mechanical particle at time, t, and specified by a continuous, single-valued, complex function known as the wave function (given by Ψ(x, t) in 1D).

Question 2

What is the polar form of a complex number (z = x + iy)?

Answer 2

r = magnitude of z (= x² + y²)
θ = phase (= arctan(y/x))

Question 3

What is the trigonometric form of a complex number (z = x + iy)?

Answer 3

R = magnitude of z (= x² + y²)
θ = phase (= arctan(y/x))

Question 4

What is postulate 1 in quantum mechanics?

Answer 4

The state of a non-relativistic quantum mechanical particle at time, t, is specified by a continuous, single-valued, complex function called the wavefunction (or state function).
The probability that the particle lies in a specific position, r, within a given volume element, dτ, at time, t, is given by the equation Ψ*(r, t)Ψ(r, t) dτ.

Question 5

What is the equation for the probability density of the location a quantum particle?

Answer 5

|Ψ(r, t)|²

∫ Ψ*(r, t)Ψ(r, t) dτ

Question 6

How is the double slit experiment related to quantum mechanics?

Answer 6

The probability of finding a particle in a given location can be found by calculating the modulus squared of the sum of the the two wavefunctions (from each slit). This results in two probability terms and an additional quantum term that depends on the phase difference between the two probability amplitudes.

Question 7

What is the time-independent form of the Schrödinger equation (not involving operators)?

Answer 7

Question 8

What is the time-dependent form of the Schrödinger equation?

Answer 8