Lecture 2

Question 1

What is the Born probablility interpretation?

Answer 1

The modulus squared of the wavefunction is proportional to the probability density for the measurement of position.

Question 2

How do you normalise a wavefunction? [red]

Answer 2

1. Identify the normalisation constant and the non normalised wave function in the given expression
2. Identify the variable in the differential and the limits of integration which corresponds to all space for the particle
3. Reason Borns probability theorum
4. Solve for C and sub back into the equation

Question 3

Does the wavefunction have to be normalised to calculate probabilities? [red]

Answer 3

Yes

Question 4

What is the first postulate of Quantum Mechanics?

Answer 4

“The state of a non-relativistic quantum particle at time t is described by a non-singular complex wavefunction, which can be normalised so that the square of its modulus is equal to the probablity density for the results of a position measurement.”

Question 5

What does it mean for a wavefunction to be normalisable?

Answer 5

Phi and its first derivative tend to zero at +/- infinity

Question 6

What is the significance of a wavefunction being continuous and non-singular?

Answer 6

• A continuous wavefunction avoids ambiguous probablilities at different positions
• A non-singular wavefunction ensures we obtain a non-infinite and non-zero normalisatino constant and avoids singularities in the wavefunction

Question 7

How do we get around the fact we cannot normalise a free particle wavefunction over +/- infinity?

Answer 7

Confine our free particle and limit all space to a large (but finite) region L.