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Flashcards in QM - Postulates of quantum Deck (19)
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1

Describe Ψ

The state of a system is fully described by a mathematical function Ψ called a wavefunction

2

Give an example of bra ket notation

3

Define a normalisation constant

A normalisation constant N is a constant such that the integral of Ψ(x)Ψ*(x) dx over all space = 1

4

Define an observable

An observable is a measurable property such as bond length or kinetic energy

5

State the postulate regarding observables and operators

Every observable B is represented by an operator B̂ and all operators can be built from the operators for position and momentum 

6

Give and describe the operator for momentum 

 p̂ 

7

Give and describe the operator for position

 x^ = multiply by x 

8

State the hamiltonian 

H^ is the total energy operator, T^ is the kinetic energy operator and V^ is the potential energy operator 

9

Show how to derive the expression for kinetic energy 

10

State the general form of an eigenvalue equation

B̂f = bf 

Where the operator B̂ acts on the eigenfunction to regenerate f multiplied by the eigenvalue b (a constant)

11

Define an exact wavefunction of the Schrodinger equation

If Ψ(x) is an eigenfunction of H^, it is termed an exact wavefunction

12

Describe orthogonal and orthonormal wavefunctions

13

Give the expectation value for an operator B̂ for a wavefunction Ψ

The expectation value is denoted by and is given below.

Note: dτ symbolises integration over all space

14

Give if the wavefunction in question is an exact wavefunction, ie an eigenfunction of H^ and also an eigenfucntion of B^ such that B^Ψ = bΨ

15

Give if the wavefunction in question is normalised

16

State the Schrodinger equation

17

State the postulate regarding 

When a system is described by a wavefunction Ψ, the average value of the observable B is equal to the expectation value of the corresponding operator B^

18

Describe the variation principle

For any trial wavefunction Ψ, the expectation energy can never be less than the energy of the ground state E0

19