130_notes.dvi

Find the (normalized) eigenvectors and eigenvalues of theSx(matrix) operator fors= 1 in the usual (Sz) basis. 6.*A spin^12 par ...

A (spin^12 ) electron is in an eigenstate ofSywith eigenvalue− ̄h 2 att= 0. The particle is in a magnetic fieldB~= (0, 0 ,B) w ...

19 Homework Problems 130A 19.1 HOMEWORK A polished Aluminum plate is hit by beams of photons of known energy. It is measured th ...

19.2 Homework Show that ∞ ∫ −∞ ψ∗(x)xψ(x)dx= ∫∞ −∞ φ∗(p) ( i ̄h ∂ ∂p ) φ(p)dp. Remember that the wave functions go to zero at ...

19.3 Homework A general one dimensional scattering problem could be characterized by an (arbitrary) poten- tialV(x) which is lo ...

19.4 Homework The 1D model of a crystal puts the following constraint on the wave numberk. cos(φ) = cos(ka) + ma^2 V 0 ̄h^2 si ...

19.5 Homework Att= 0, a 1D harmonic oscillator is in a linear combination of the energy eigenstates ψ= √ 2 5 u 3 +i √ 3 5 u 4 ...

19.6 Homework The energy spectrum of hydrogen can be written in terms of theprincipal quantum number nto beE=−α (^2) μc 2 2 n^ ...

19.7 Homework A particle is in the stateψ=R(r) (√ 1 3 Y^21 +i √ 1 3 Y^20 − √ 1 3 Y^22 ) . Find the expected values of L^2 ,Lz, ...

19.8 Homework Calculate theℓ= 0 phase shift for the spherical potential well for both and attractive and repulsive potential. C ...

19.9 Homework An electron in the Hydrogen potentialV(r) =−e 2 r is in the stateψ(~r) =Ce −αr. Find the value ofCthat properly ...

20 Electrons in an Electromagnetic Field In this section, we will study the interactions of electrons in an electromagnetic fiel ...

If we derive the fields frompotentials, B~ = ∇×~ A~ E~ = −∇~φ−^1 c ∂A ∂t then the first two Maxwell equations are automatically ...

in the usual way, by replacing the momentum by the momentum operator, for the case of a constant magnetic field. Note that the m ...

In the example below, we will solve the Quantum Mechanics problem twoways: one using our new Hamiltonian with B field terms, and ...

This is just thestandard gauge transformation of electromagnetism, but, we now see that local phase symmetry of the wavefunction ...

Flux is observed to be quantized but the charge of the particle seenis 2e. Φ = 2 nπ ̄hc 2 e This is due to the pairing of electr ...

slits interfereψ=ψ 1 +ψ 2. Let’s start withB= 0 andA= 0 everywhere. When we change theB field, the wavefunctions must change. ψ ...

Hamiltonian and will give constants of the motion. We therefore will beable to separate variables in the usual way. ψ(~r) =unmk( ...

~∇×B~−^1 c ∂E ∂t = 4 π c J~ ∂ ∂xi Bjǫijk− 1 c ∂Ek ∂t = 4 π c Jk B~=∇×~ A~ Bj= ∂ ∂xm Anǫmnj E~=−~∇φ−^1 c ∂A ∂t Ek=− ∂ ∂xk φ− 1 c ...