The Hong Kong University of Science and Technology
PHYS
PHYS 3122

Fall 2015
PHYS3036 Spring 2016
Elementary Quantum Mechanics I
Tutorial II
Feb. 22, 2016
1. Griffiths Problem 2.18
2. Griffiths Problem 2.23
Homework II
Due Tue March 1, 2016 before 6pm
Hand in to my office in Rm4438. Do not hand in to any TA/IA.
WARNING: You are en
The Hong Kong University of Science and Technology
PHYS
PHYS 3122

Fall 2015
Chapter 3 Ordinary differential equations
1
Firstorder differential equations with one variable
The simple types of ordinary differential equation (ODE) is a firstorder equation with one variables,
such as,
dx
2x
=
dt
t
This equation can be solved by ha
The Hong Kong University of Science and Technology
PHYS
PHYS 3122

Fall 2015
Chapter 4 Partial Differential Equation
1
Introduction
As with ordinary differential equation, problems involving partial differential equations can be divided
into initial value problems and boundary value problems.
Boundary value problems
We have a part
The Hong Kong University of Science and Technology
PHYS
PHYS 3122

Fall 2015
Chapter 2 Solution of linear and nonlinear equations
1
Simultaneous Linear Equations
A single linear equation in one variable, such as x 1 = 0, is trivial to solve. But simultaneous sets
of linear equations in many variables are harder. In principle the t
The Hong Kong University of Science and Technology
PHYS
PHYS 3122

Fall 2015
Monte Carlo
Random number
Good random numbers play a central part in Monte Carlo simula5ons.
Usually these are generated using a determinis5c algorithm; the numbers
generated this way are called pseudorandom numbers.
T
The Hong Kong University of Science and Technology
PHYS
PHYS 3122

Fall 2015
PHYS 3142 Sping 2016
Computational Methods in Physics
Lab 8
Due: 18th April 2016
Quantum oscillators
Consider the onedimensional, timeindependent Schrdinger equation in a harmonic (i.e.,
quadratic) potential V ( x ) = V0 x2 /a2 , where V0 and a are cons
The Hong Kong University of Science and Technology
PHYS
PHYS 3122

Fall 2015
PHYS 3142 Sping 2016
Computational Methods in Physics
Lab 3
Due: 7 th March 2016
(1) In this question, we want to compute the following integral
Z 1
dx
p
I=
sin(x)
0
(1)
where the integrand is infinite at x = 0.
(a) Compute the integral by applying the me
The Hong Kong University of Science and Technology
PHYS
PHYS 3122

Fall 2015
PHYS 3142 Sping 2016
Computational Methods in Physics
Lab 7
Due: 11th April 2016
1. A lowpass filter
Here is a simple electronic circuit with one resistor and one capacitor:
R
I
Vin
Vout
C
0
This circuit acts as a lowpass filter: you send a signal in on
The Hong Kong University of Science and Technology
PHYS
PHYS 3122

Fall 2015
PHYS 3142 Sping 2016
Computational Methods in Physics
Lab 5
Due: 21st March 2016
(1) Warm up Exercise  One variable nonlinear equation: Consider a nonlinear equation:
5ex + x 5 = 0
(a) Write a program to solve this equation for positive x to an accuracy
The Hong Kong University of Science and Technology
PHYS
PHYS 3122

Fall 2015
Chapter 1
Integral and Derivative
1
Taylor series
Taylor series is an essential concept in understanding numerical methods. Examples include finding
accuracy of divided difference approximation of derivatives, forming the basis for Romberg method
of numer