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# PHYC40020

#### Applied Quantum Mechanics (PHYC40020)

Subject:
Physics
College:
Science
School:
Physics
Level:
4 (Masters)
Credits:
5
Module Coordinator:
Dr Antonio Benedetto
Trimester:
Autumn
Mode of Delivery:
Blended
Internship Module:
No

Curricular information is subject to change.

The module will build upon PHYC30030. The following list of topics will be covered: Topics covered in this course include the time-dependent Schrodinger equation; the variational principle; position and momentum operators and representations (Fourier transforms); a complete treatment of the Stern-Gerlach experiment; spin; quantum dynamics; Heisenberg operators and equation of motion; two state quantum systems; spin precession in a magnetic field; ammonia molecule in an electric field, and the MASER (Nobel Prize work); nuclear magnetic resonance (Nobel Prize work); multiparticle states and tensor product; entangled states and quantum teleportation; EPR paradox and Bell Inequality.

###### Learning Outcomes:

On completion of this module students should be have complete picture of quantum physics, and be able to apply fundamental quantum mechanics to physical systems. They should have an appreciation of how these theoretical models relate to experimentally determined quantities, and about edge applications of quantum physics.

###### Indicative Module Content:

The time-dependent Schrodinger equation
The probability density and the probability current
The normalization of the wavefunction
The time-independent Schrodinger equation and stationary solutions
Energy eigenstates and eigenfunctions
Orthonormal basis
Wavefunctions as linear combination of eigenfunctions and their time evolution
Expectation values
Energy eigenstates in one dimension
The variational principle (with few examples)
Vector representation of wavefunctions
Position and momentum operators, eigenstates and eigenfunctions
Matrix representations of the position and momentum operators
Momentum representation (Fourier transforms)
Overview of linear algebra (e.g. hermitian and unitary operators, complex vector space) Bra and Ket notation, and inner product
The Stern-Gerlach experiment (complete derivation)
Spin one-half states and operators, vector and matrix representations
Pauli matrices
Spin states in arbitrary directions
Quantum dynamics
Schrodinger dynamics representation
Unitary time evolution operator
Derivation of the Schrodinger equation
Derivation of the unitary time evolution operator
Heisenberg dynamics representation
Heisenberg operators and equation of motion
Examples of Schrodinger and Heisenberg representations (e.g. harmonic oscillator)
Two state systems case and the vector representation of the Schrodinger equation
Spin precession in a magnetic field
The ammonia molecule
Ammonia molecule in an electric field, and the MASER (Nobel Prize work)
Nuclear Magnetic Resonance and Magnetic Resonance Imaging (Nobel Prize work)
Multiparticle states and tensor product
Entangled states
Bell basis states
Quantum teleportation
Bell Inequality
Introduction to quantum information theory
Introduction to quantum biology
Time dependent perturbation theory
Scattering theory, and neutron scattering
Dirac equation

###### Student Effort Hours:
Student Effort Type Hours
Lectures

36

Seminar (or Webinar)

1

Specified Learning Activities

15

Autonomous Student Learning

72

Total

124

###### Approaches to Teaching and Learning:
Lectures; continuous assessment, which may include student presentations (in small groups)
Requirements, Exclusions and Recommendations
Learning Requirements:

Students should have taken PHYC 30030 or equivalent

Module Requisites and Incompatibles
Not applicable to this module.

Assessment Strategy
Description Timing Open Book Exam Component Scale Must Pass Component % of Final Grade In Module Component Repeat Offered
Continuous Assessment: MCQs, classwork and homework. It may include student presentations (in small groups) Varies over the Trimester n/a Standard conversion grade scale 40% No

30

No
Examination: End of semester written exam 2 hour End of Trimester Exam No Standard conversion grade scale 40% No

70

Yes

Carry forward of passed components
No

Resit In Terminal Exam
Spring Yes - 2 Hour
###### Feedback Strategy/Strategies

• Group/class feedback, post-assessment
• Self-assessment activities

###### How will my Feedback be Delivered?

Not yet recorded.

Required textbooks:
- Griffiths David J. and Darrell F. Schroeter, Introduction to Quantum Mechanics, 3rd edition
- Shankar Ramamurti, Principles of Quantum Mechanics, 2nd Edition

Other textbooks:
- Dirac P.A.M., The Principles of Quantum Mechanics
- Feynman R.P., Feynman Lectures On Physics, Vol. 3 Quantum Mechanics