The Hong Kong University of Science and Technology
Quantum Mechanics I
PHYSICS 3036

Spring 2016
Chapter 1 The Wave Function
( x, t )
Borns Statistical Interpretation (for interpreting a wave as a particle)
2
( x, t ) dx probability of finding the particle between x and x+dx at time t
What exactly is probability density (histogram in discrete case)
c
The Hong Kong University of Science and Technology
Quantum Mechanics I
PHYSICS 3036

Spring 2016
Intended Learning Outcomes of this lecture:
After this lecture you can
1. write down the stationary state energy levels and wavefunctions of a harmonic
oscillator.
2. list out properties which are in common between the set of all eigenfunctions of a
harmo
The Hong Kong University of Science and Technology
Quantum Mechanics I
PHYSICS 3036

Spring 2016
Intended Learning Outcomes for revision:
After this lecture you can
1. describe the physical meaning of bound and scattering states.
2. tell the mathematical condition that distinguishes between a bound and scattering
state in terms of it energy.
3. do si
The Hong Kong University of Science and Technology
Quantum Mechanics I
PHYSICS 3036

Spring 2016
Intended Learning Outcomes for revision:
After this lecture you can
1. simplify a problem when the potential function is even.
2. find the bound state energy and wavefunction of the finite square well.
3. sketch the energy spectrum of a finite square well
The Hong Kong University of Science and Technology
Quantum Mechanics I
PHYSICS 3036

Spring 2016
Chapter 3 Formalism
Intended Learning Outcomes for revision:
After this lecture you can
1. explain Diracs formulation of quantum mechanics by treating states (or
wavefunctions) of a QM system as elements in a linear space called Hilbert space.
2. use the
The Hong Kong University of Science and Technology
Quantum Mechanics I
PHYSICS 3036

Spring 2016
Intended Learning Outcomes for revision:
After this lecture you can
1. make prediction (possible outcomes and corresponding probabilities) about
measuring a quantity Q on a quantum state .
2. write down the state after a measurement is made provided the m
The Hong Kong University of Science and Technology
Quantum Mechanics I
PHYSICS 3036

Spring 2016
Revision on Dirac bracket notation
Make sure you distinguish among the following quantities:
A vector in the Hilbert space, i.e., a wavefunction (physically
Ket
allowed state)
Bra
Dual vector of , defined as * dx (a functional)
Bracket 1 2
A scalar defi
The Hong Kong University of Science and Technology
Quantum Mechanics I
PHYSICS 3036

Spring 2016
Review (for your own revision)
A wavefunction ( x, t ) must satisfy the timedependent Schrdinger equation
d
V
i
H where H
2m dx 2
t
2
Hamiltonian
2
KE operator
PE operator
If V ( x) is _, then try ( x, t ) of the form
( x, t ) eiEt / ( x)
solution to
The Hong Kong University of Science and Technology
Quantum Mechanics I
PHYSICS 3036

Spring 2016
Chapter 2 The Timeindependent Schrdinger Equation
Intended Learning Outcomes of this lecture:
After this lecture you can
1. Explain what a stationary problem is.
2. Distinguish between the timedependent and timeindependent Schrdinger
equations.
3. Desc