### Syllabus

Summary of Schrodinger picture. Heisenberg picture, equations of motion,

The interaction picture. Time evolution of states and observables in

interaction picture.

### Prerequisites

Desription of states as vectors in Hilbert space.

Unitary and Hermitian operators.

Functions of Operators. Time development of states.

Time evolution of averages, stationary states.

### Instruction Goals

To explain the following:

- What is meant by a picture (of time evolution)in quantum theory?
- Why is that we have different pictures of time evolution?
- Schrodinger, Heisenberg and Dirac (interaction) pictures of quantum mechanics. How are they defined and what connects them?
- How are the three pictures of quantum mechanics different?
- How to write (formal) solutions of equations of motion in the three pictures.

### Lessons

- States and Observables in Quantum Mechanics
- Schrodinger Picture
- Heisenberg Picture
- Dirac Picture
- Perturbation Expansion in Interaction Picture

### Suggested Questions and Problems

- Quick check of Schrodinger picture; stationary states and constants of motion.
- Solving EOM in Heisenberg picture
- Computing the interaction Hamiltonian in interaction picture.
- Unequal time Commutators;

### Where do we need all, or some part, of this unit

- Evolution of free particle wave packets
- Propagator in quantum mechanics
- Approximation methods for time dependent problems
- Lowest order transitions and transition amplitudes.
- Transition to continuum states; Fermi Golden Rule Scattering cross section.

### Notes and References

The interaction picture gives and elegant way of doing time dependent

perturbation theory in quantum mechanics and quantum field theory.

The interaction picture is extensively used in relativistic quantum field

theory.

### Planned for Next Phase

To draw flow charts, concept maps.

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### Exclude node summary :

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