PHYS 30101 Quantum Mechanics the dreams stuff is made of

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PHYS 30101 Quantum Mechanicsthe dreams stuff
is made of
Dr Jon Billowes Nuclear Physics Group (Schuster
Building, room 4.10) j.billowes_at_manchester.ac.uk
These slides at www.man.ac.uk/dalton/phys30101
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PC3101 Quantum Mechanics Recommended texts A.I.M
Rae, Quantum Mechanics (4th edition, IOP) F.
Mandl, Quantum Mechanics P.C.W. Davies, Quantum
Mechanics A.P. French E.F. Taylor, An Intro. To
Quantum Mechanics Beyond level of course S.
Gasiorowicz, Quantum Mechanics
(but recommended for
PC3602) supplementary material has moved to
www.crcpress.com/e_products/downloads/webdownload/
IP6095CRAEextra.pdf
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• Syllabus
• Basics of quantum mechanics (QM) Postulate,
  operators, eigenvalues eigenfunctions,
  orthogonality completeness, time-dependent
  Schrödinger equation, probabilistic
  interpretation, compatibility of observables,
  the uncertainty principle.
• 1-D QM Bound states, potential barriers,
  tunnelling phenomena.
• Orbital angular momentum Commutation relations,
  eigenvalues of Lz and L2, explicit forms of Lz
  and L2 in spherical polar coordinates, spherical
  harmonics Yl,m.
• Spin Noncommutativity of spin operators, ladder
  operators, Dirac notation, Pauli spin matrices,
  the Stern-Gerlach experiment.
• Addition of angular momentum Total angular
  momentum operators, eigenvalues and
  eigenfunctions of Jz and J2.
• The hydrogen atom revisited Spin-orbit coupling,
  fine structure, Zeeman effect.
• Perturbation theory First-order perturbation
  theory for energy levels.
• Conceptual problems The EPR paradox, Bells
  inequalities.

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The Schrödinger Equation was guessed by
induction Seemed plausible test
works OK, accept until falsified
Classical plane wave (sound or light)
obeys the wave equation
The solution requires
But does not work for matter waves where we want
Requires 2nd derivative of x but only 1st
derivative of t
(TDSE Time-dependent Schrödinger equation)
Idea! Lets try
No prediction of quantum mechanics has ever been
experimentally falsified
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Wave-particle duality applies to all objects
screen
Particle detected at single point on the screen
the probability wave instantaneously collapses to
zero everywhere else.
particle
If undisturbed, the particle propagates as a
(probability) wave. Development of the wave with
time is exactly described by the TDSE
http//www.hqrd.hitachi.co.jp/em/doubleslit.cfm
Electron interference
Quantum interference experiments Single photons
? electrons ? neutrons ? atoms ?
Buckminster fullerene (C60) ?
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Conceptual problems with quantum mechanics
Quantum mechanics works - but there are many
worries on interpretation that tend to become
matters of opinion debate enters realm of
philosophy. Conceptual basis of QM is fundamental
to our understanding of the nature of the
physical universe so we should try and learn
more by experiment, not debate (EPR paradox and
Bells inequalities). Alastair Rae (in 4th
edition of his text book) my own understanding
continues to grow Richard Feynman I think
I can safely say that nobody understands quantum
mechanics. Niels Bohr Anyone who is not
shocked by quantum mechanics has not understood
it. Feynman (again) shut up and calculate.
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After revision of basics, first new topic will
be Quantum Mechanical Tunnelling
Consider a roller-coaster Classically the car
can only go as far As C before rolling back but
quantum-fluctuations in energy could allow the
car through the energy-forbidden region and
appear at E.
This quantum process controls the rates of
alpha-decay and spontaneous fission in nuclear
physics.
Application Scanning tunnelling microscope
Iron atoms on copper
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Useful formulae
TDSE time dependent Schrödinger Equation
TISE time independent S.E.
Vector operators in spherical polar coordinates
Angular momentum operators in spherical polars
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Plan of action

• Basics of QM
• 1D QM

Will be covered in the following order
1.1 Some light revision and reminders 1.2 TISE
applied to finite wells 1.3 TISE applied to
barriers tunnelling phenomena 1.4 Postulates of
QM (i) What ? represents (ii) Hermitian
operators for dynamical variables (iii)
Operators for position, momentum, ang. mom. (iv)
Result of measurement 1.5 Commutators,
compatibility, uncertainty principle 1.6
Time-dependence of ?