14. The Postulates Flashcards
What variables is a classical system defined by?
A list of dynamical variables
How are dynamical variables updated classically and give an example
By equations of motion
- e.g. Hooke’s law, Newton’s laws etc
What proportion of the classical dynamical variables are we allowed to know in a system at a given time?
All of them all of the time
How do classical dynamical variables evolve?
According to equaitons of motion
What can be said about the evolution of dynamical variables in a classical system?
The evolution is deterministic
How is a QM system NOT defined?
By the values of its dynamical variables
How is a state in QM defined?
By a state/wave function
What is the QM equation of motion showing how states evolve?
The TDSE
Is the TDSE non-relativistic?
Yes
See p6 in document for TDSE equation
Do it
How are dynamical variables connected to the wave function?
By measurement
Give an example of a limitation when measuring a dynamical system in QM
HUP
When (and only when) can a QM system evolve (TDSE)?
When no measurements are being made on the system
Briefly outline the first postulate (1stP) of QM
For every dynamical system, there exists a state function from which all possible predictions of the physical properties can be obtained
1stP: Describe the state function mathematically
Continuous, non-singular, square-integrable, single-valued and normalisable
(2ndP) Define observables
Observables are dynamical variables of a quantum system accessible to measurement
(2ndP) what are each observables associated with?
An operator which must be linear and Hermitian
Briefly outline the third postulate (3rdP) of QM
When a measurement is made of a dynamical variable, the result is one of the eigenvalues of the operator Q_hat.
- PROBABILISTIC
Briefly outline the fourth postulate (4thP) of QM
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
See page 6 of document for a mathatical representation of the expectation value for the 4thP
Do it
Briefly outline the fifth postulate (5thP) of QM
The time dependence of the wave function is determined by the TDSE
See page 7 of document for a mathematical representation of the 5thP
Do it lmao
What is the equation of motion for a quantum state provided what does not happen?
The TDSE provided a no measurements are made
