QM Lecture 10 Part 1

Part 1

10.1   Representation of the wavefunction in the spatial and momentum coordinates
          10.1.A   Representation of the wavefunction  in the basis of spatial coordinates basis {  / x>}
                      10.1.A1  The Delta Dirac
                      10.1.A2  Compatibility between the physical concept of amplitude probability and the notation used for the inner product.
          10.1.B    Representation of the wavefunction  in the momentum coordinates basis {  / p> }
                      10.1.B1  Representation of the /p >  state in space-coordinates  basis { / x > }
                      10.1.B2  Identifying the amplitude probability/p>  as the Fourier transform of the function (x)
10.2   The Schrödinger Equation as a postulate
          10.2.A   The Hamiltonian equations expressed in the continuum spatial coordinates.
                      The Schrodinger Equation.
          10.2.B   Interpretation of the Wavefunction
                      Einstein’s view on the granularity nature of the electromagnetic radiation.
                      Max Born’s probabilistic interpretation of the wavefunction.
                      Deterministic evolution of the wavefunction
                      Ensemble
          10.2.C   Normalization condition of the wavefunction
                      Hilbert space
                      Conservation of probability
          10.2.D   The Philosophy of  Quantum Theory
10.3   Expectation values
          10.3.A  Expectation value of a particle’s position
          10.3.B  Expectation value of the particle’s momentum
          10.3.C  Expectation (average) values are calculated in an ensemble of identically prepared systems
10.4   Operators associated to observables
          10.4.A  Observables, eigenvalues and eigenstates
          10.4.B  Definition of the quantum mechanics operator   to be associated with the observable physical quantity  f
          10.4.C  Definition of the Position Operator
          10.4.D  Definition of the Linear Momentum Operator     
                      10.4.D.1  Representation of the linear momentum operator   in the momentum basis
                      10.4.D.2  Representation of the linear momentum operator   in the spatial coordinates basis
                      10.4.D3  Construction of the operators 
          10.4.E  The Hamiltonian operator
                      10.4.E.1 Evaluation of the mean energy in terms of the Hamiltonian operator
                      10.4.E.2 Representation of the Hamiltonian operator in the spatial coordinate basis