14. The Postulates

Question 1

What variables is a classical system defined by?

Answer 1

A list of dynamical variables

Question 2

How are dynamical variables updated classically and give an example

Answer 2

By equations of motion

- e.g. Hooke’s law, Newton’s laws etc

Question 3

What proportion of the classical dynamical variables are we allowed to know in a system at a given time?

Answer 3

All of them all of the time

Question 4

How do classical dynamical variables evolve?

Answer 4

According to equaitons of motion

Question 5

What can be said about the evolution of dynamical variables in a classical system?

Answer 5

The evolution is deterministic

Question 6

How is a QM system NOT defined?

Answer 6

By the values of its dynamical variables

Question 7

How is a state in QM defined?

Answer 7

By a state/wave function

Question 8

What is the QM equation of motion showing how states evolve?

Answer 8

The TDSE

Question 9

Is the TDSE non-relativistic?

Answer 9

Yes

Question 10

See p6 in document for TDSE equation

Answer 10

Do it

Question 11

How are dynamical variables connected to the wave function?

Answer 11

By measurement

Question 12

Give an example of a limitation when measuring a dynamical system in QM

Answer 12

HUP

Question 13

When (and only when) can a QM system evolve (TDSE)?

Answer 13

When no measurements are being made on the system

Question 14

Briefly outline the first postulate (1stP) of QM

Answer 14

For every dynamical system, there exists a state function from which all possible predictions of the physical properties can be obtained

Question 15

1stP: Describe the state function mathematically

Answer 15

Continuous, non-singular, square-integrable, single-valued and normalisable

Question 16

(2ndP) Define observables

Answer 16

Observables are dynamical variables of a quantum system accessible to measurement

Question 17

(2ndP) what are each observables associated with?

Answer 17

An operator which must be linear and Hermitian

Question 18

Briefly outline the third postulate (3rdP) of QM

Answer 18

When a measurement is made of a dynamical variable, the result is one of the eigenvalues of the operator Q_hat.
- PROBABILISTIC

Question 19

Briefly outline the fourth postulate (4thP) of QM

Answer 19

The expectation value of the observable, Q_hat is obtained by taking the mean of an observable measured over many experiments starting with the same quantum state

Question 20

See page 6 of document for a mathatical representation of the expectation value for the 4thP

Answer 20

Do it

Question 21

Briefly outline the fifth postulate (5thP) of QM

Answer 21

The time dependence of the wave function is determined by the TDSE

Question 22

See page 7 of document for a mathematical representation of the 5thP

Answer 22

Do it lmao

Question 23

What is the equation of motion for a quantum state provided what does not happen?

Answer 23

The TDSE provided a no measurements are made