PHYS Quantum Mechanics PHYS Quantum Mechanics Dr Jon Billowes Nuclear Physics Group (Schuster Building, room 4.10) These slides at: Lecture 5

Plan of action 1.Basics of QM 2.1D QM Will be covered in the following order: 1.1 Some light revision and reminders. Infinite well 1.2 TISE applied to finite wells 1.3 TISE applied to barriers – tunnelling phenomena 1.4 Postulates of QM (i) What Ψ 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 Ψ

Ψ = general solution to TDSE u, u n = time-independent part of Ψ ψ = general wavefunction whose time-dependence is not being considered φ, φ n = eigenfunction of an operator, not necessarily the energy operator (Hamiltonian)

Dynamical variable = a measurable quantity (position, momentum, angular momentum, energy). Ĥ Ĵ ĴzĴz Energy (KE + PE) Angular momentum (orbital + spin) Z-component of angular momentum

Summary of postulates 1.A quantum system has a wavefunction associated with it. 2.When a measurement is made, the result is one of the eigenvalues of the operator associated with the measurement. 3.As a result of the measurement the wavefunction “collapses” into the corresponding eigenfunction. 4.The probability of a particular outcome equals the square of the modulus of the overlap between the wavefunction before and after the measurement.