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Quantum mechanics unit 1

Quantum mechanics unit 1. Foundations of QM Photoelectric effect, Compton effect, Matter waves The uncertainty principle The Schr ö dinger eqn. in 1D Square well potentials and 1D tunnelling The harmonic oscillator. www2.le.ac.uk/departments/physics/people/academic-staff/mr6/lectures.

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Quantum mechanics unit 1

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  1. Quantum mechanics unit 1 • Foundations of QM • Photoelectric effect, Compton effect, Matter waves • The uncertainty principle • The Schrödinger eqn. in 1D • Square well potentials and 1D tunnelling • The harmonic oscillator www2.le.ac.uk/departments/physics/people/academic-staff/mr6/lectures

  2. Last time • Solving the Schrödinger equation (for given ) • Examine the physics • Write down the solution to the S.E. (which will generally contain some arbitrary constants) • Apply the boundary conditions and normalise the wavefunctionto find the unknown constants • Find the allowed energies and the probability density

  3. Finite square well www2.le.ac.uk/departments/physics/people/academic-staff/mr6/lectures

  4. Graphical solution: Even parity states

  5. Graphical solution: Odd parity states

  6. Compare infinite to finite well Well half width, Å, Finite well depth, eV Infinite well eV eV eV … Finite well eV eV eV eV

  7. Quantum tunnelling

  8. Quantum tunnelling

  9. Tunnelling of classical waves Tippler – 35.4 Reflection and transmission of electron waves: Barrier penetration

  10. Tunnelling of classical waves

  11. Tunnelling through a barrier

  12. Tunnelling through a barrier • Write down solutions to S.E. • Apply boundary conditions at , • Eliminate coefficients - see notes at www2.le.ac.uk/departments/physics/people/academic-staff/mr6/lectures • Find

  13. Å eV

  14. Tunnelling through a barrier • Transmission probability is • Large barrier, then • General case if

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