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Chapter06 Quantum Mechanics II

Chapter06 Quantum Mechanics II. General Bibliography 1) Various wikipedia, as specified 2) Thornton-Rex, Modern Physics for Scientists & Eng, as indicated. Postulates of Quantum Mechanics. All information that can be known about a particle/system is contained within the wavefunction Y (x,t)

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Chapter06 Quantum Mechanics II

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  1. Chapter06Quantum Mechanics II General Bibliography 1) Various wikipedia, as specified 2) Thornton-Rex, Modern Physics for Scientists & Eng, as indicated

  2. Postulates of Quantum Mechanics • All information that can be known about a particle/system is contained within the wavefunction Y(x,t) • The probability of finding the particle at (x,t) is given by Y* Y. • in a region Dx about (x,t) by Y* Y Dx • The probability of finding the particle anywhere is 100% or 1.

  3. Postulates of Quantum Mechanics H = Hamiltonian Every observable quantity is associated with an “Operator” which is used to extract the information from the wavefunction The expectation value (aka average) of an observable quantity is given by The time evolution of the wavefunction is determined by

  4. Example Functions • Can it be a solution to the time-dependent Schroedinger Eqn?

  5. Properties of Good Wavefunctions • Y must be finite everywhere • Y must be single-valued • Y and dY/dx must be continuous for finite well-behaved potentials V(x) • Y must be normalizable (generally Y0 as xinf)

  6. Infinite Square Well

  7. Infinite Square Well

  8. 6.4 Finite Square Well

  9. 6.5 3-D Finite Square Well

  10. 6.6 Simple Harmonic Oscillator

  11. For Etot less than barrier height

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