. Non-Inertial Co-ordinate systems
A co-ordinate system fixed in the Earth is not an inertial
system since Earth it self is rotating in space. There are
many important effects that result from the non inertial
nature of the Earths co-ordinate system.
Let

41
The Time-Dependent Schrodinger Equation (TDSE)
This basic equation of non-relativistic quantum mechanics was proposed by E. Schrodinger in 1926
and is also called the wave equation.
r
(r , t )
t
r
H (r , t ) , where H
h2 2
r
V (r , t )
2m
( x,

1
PH 3001 - Quantum Mechanics I
Tutorial
The Uncertainty Principle
1. (a) State the two commonly used forms of the uncertainty principle and give a brief explanation of
each of them.
(b) Why is the effect of the uncertainty principle not noticeable in our

PH 4010 - Quantum Mechanics II
Tutorial
1. When proving that the Ehrenfest's equations are equivalent to Newton's equations of motion
one has to use the fact that F(x) = F(x). Discuss under what circumstances this
condition is approximately valid. (Read p

Rigid Body Motion
A rigid body is defined as a collection of particles
whose relative distances are constrained to remain fixed
regardless of forces acting on it.
Such bodies do not exist in nature since the atoms which
comprises the body undergoes some r

Hamiltonian Theory
A superstructure on Lagrangian theory known
as the Hamiltonian theory was constructed by
an Irish mathematician and physicist Sir
William Rowan Hamilton (1805-1865).
Hamiltonian formulation like the Lagrangian formulation
is based on th

Canonical Transformations
In many cases it is impossible to solve Hamiltonian
equations of motion. One way to simplify the equations of
motion may be through a transformation of coordinates.
Sometimes in a particular dynamical problem it is
convenient t

Theory of Small Oscillations
A common form of motion of mechanical systems is small
oscillations of a system about the position of stable
equilibrium.
The theory of small oscillations is in general an
approximate theory of the motion of mechanical or phys

Hamiltons Principle
One of the most important integral
principle in classical mechanics known
as the Hamiltons principle was
introduced in 1833 by Sir William R.
Hamilton. The method of dealing with
complicated problems in a general
manner in Hamiltonian

Hamilton - Jacobi Theory
In physics, the HamiltonJacobi equation (HJE) is a
reformulation of classical mechanics and, equivalent
to other formulations such as Newtons Law of motion,
Lagrangian mechanics and Hamiltonian mechanics.
The HamiltonJacobi equa

81
Motion in Three-Dimension
(9) Free Particle (3-d)
Consider a particle of mass m moving in a region of constant potential energy
r
V r V x, y, z V0 ( 0) , in the region x , y , z .
h2 2 r
r
2m
TISE
r
E r
r
r x x y y z z and the corresponding energy