Chem 249 Problem Set 2

... 3. Consider an anharmonic oscillator with the following Hamiltonian: H = H0 + W H0 = p2/2m + kx2/2 W = x3 a. Calculate the energies of H to first order in the perturbation W. Write out formally the first order correction to the eigenstate vector, and then list the states which contribute to the ne ...

... 3. Consider an anharmonic oscillator with the following Hamiltonian: H = H0 + W H0 = p2/2m + kx2/2 W = x3 a. Calculate the energies of H to first order in the perturbation W. Write out formally the first order correction to the eigenstate vector, and then list the states which contribute to the ne ...

Thirteenth quantum mechanics sheet

... is spanned by the product of Eigenstates of Ŝ3 and the Eigenstates |n, l, ml i of Ĥ0 , L |n, l, ml , ms i := |n, l, ml i|ms i ~ ·S ~ commutes with L ~ 2 and S ~ 2 , but not with L3 and S3 . (4 points) a) Show that Ŵ ∼ L This means that the product state |n, l, ml , ms i does not build an appropri ...

... is spanned by the product of Eigenstates of Ŝ3 and the Eigenstates |n, l, ml i of Ĥ0 , L |n, l, ml , ms i := |n, l, ml i|ms i ~ ·S ~ commutes with L ~ 2 and S ~ 2 , but not with L3 and S3 . (4 points) a) Show that Ŵ ∼ L This means that the product state |n, l, ml , ms i does not build an appropri ...

another Exam2

... (c) (5) Now consider the 3-dimensional delta-function potential V (r ) = A ! (r) . Using the first Born approximation again, calculate d! / d" . Determine the constant A which gives the same result as was found in part (b). ...

... (c) (5) Now consider the 3-dimensional delta-function potential V (r ) = A ! (r) . Using the first Born approximation again, calculate d! / d" . Determine the constant A which gives the same result as was found in part (b). ...

Problem-set10 32. Polarization of atomic hydrogen in the vicinity of a

... This is the standard textbook problem so I will just ask you to go over yourself following these steps. (a) Write down the Hamiltonian for the two electrons in the helium atom, neglecting the spin-orbit interaction. (b) Assume that the electron-electron interaction is small, we will treat this term ...

... This is the standard textbook problem so I will just ask you to go over yourself following these steps. (a) Write down the Hamiltonian for the two electrons in the helium atom, neglecting the spin-orbit interaction. (b) Assume that the electron-electron interaction is small, we will treat this term ...

Chemistry 681 Introduction to Quantum

... • Qualitative analysis of 1D systems. • Particle-in-a-box. • Harmonic oscillator. • 1D scattering. Barriers and tunneling. • Particle-on-a-ring. 5. QM in 3 dimensions • Particle-on-a-sphere and angular momentum. • Two particles in 3D. Central force problem. • H atom. 6. Approximate methods in time-i ...

... • Qualitative analysis of 1D systems. • Particle-in-a-box. • Harmonic oscillator. • 1D scattering. Barriers and tunneling. • Particle-on-a-ring. 5. QM in 3 dimensions • Particle-on-a-sphere and angular momentum. • Two particles in 3D. Central force problem. • H atom. 6. Approximate methods in time-i ...

energy levels of a hydrogen atom in crossed electric and

... respectively. The energy level splitting was hence easily obtained. It is surprising that, as far as we know, this important problem was not considered after the establishment of quantum mechanics, apparently because it was not apparent that its solution is difficult in principle, and at the same ti ...

... respectively. The energy level splitting was hence easily obtained. It is surprising that, as far as we know, this important problem was not considered after the establishment of quantum mechanics, apparently because it was not apparent that its solution is difficult in principle, and at the same ti ...

(Quantum Mechanics) 1. State basic concepts (or postulates) of

... 6. Find out the eigenstates and eigenvalues of a point mass of in an infinite well of a width of . Draw the wave functions of the lowest three states. 7. Draw the (schematic) wavefunctions of the lowest three states in a finite well of width . 8. A particle with mass and energy moves from ...

... 6. Find out the eigenstates and eigenvalues of a point mass of in an infinite well of a width of . Draw the wave functions of the lowest three states. 7. Draw the (schematic) wavefunctions of the lowest three states in a finite well of width . 8. A particle with mass and energy moves from ...

Lecture 17

... We need to compute the matrix Vij in the subspace of the unperturbed states of the H atom with n = 2. This is a 4 × 4 Hermitean matrix. Note that the perturbation V is odd under parity, and therefore it has non-vanishing matrix elements only between states of opposite parity. Since the eigenstates o ...

... We need to compute the matrix Vij in the subspace of the unperturbed states of the H atom with n = 2. This is a 4 × 4 Hermitean matrix. Note that the perturbation V is odd under parity, and therefore it has non-vanishing matrix elements only between states of opposite parity. Since the eigenstates o ...

Interaction with the radiation field

... => the so-called The Lorentz Oscillator => large portion of the observed effects in atom-field interactions not supported (e.g quantized transitions) – QM model needed! ...

... => the so-called The Lorentz Oscillator => large portion of the observed effects in atom-field interactions not supported (e.g quantized transitions) – QM model needed! ...

1 Rayleigh-Schrödinger Perturbation Theory

... Expansions for the higher order corrections to Ψn may be obtained in a similar manner with increasingly complicated expressions for the expansion coefficients. These expressions for the perturbed wavefunction lead directly to the perturbed energies via equation (20). At this point it is interesting ...

... Expansions for the higher order corrections to Ψn may be obtained in a similar manner with increasingly complicated expressions for the expansion coefficients. These expressions for the perturbed wavefunction lead directly to the perturbed energies via equation (20). At this point it is interesting ...