LOYOLA COLLEGE (AUTONOMOUS), CHENNAI – 600 034

... 16. State and prove Ehernfest’s theorem 17. Solve the Schrodinger equation for a linear harmonic oscillator. Sketch the first two eigenfunctions of the system. 18. Determine the eigenvalue spectrum of angular momentum operators Jz and Jz 19. What are symmetric and antisymmetric wave functions? Show ...

... 16. State and prove Ehernfest’s theorem 17. Solve the Schrodinger equation for a linear harmonic oscillator. Sketch the first two eigenfunctions of the system. 18. Determine the eigenvalue spectrum of angular momentum operators Jz and Jz 19. What are symmetric and antisymmetric wave functions? Show ...

ph 2811 / 2808 - quantum mechanics

... 6. State and prove Ehernfest’s theorem 7. Solve the Schrodinger equation for a linear harmonic oscillator. Sketch the first two eigenfunctions of the system. 8. Determine the eigenvalue spectrum of angular momentum operators Jz and Jz 9. What are symmetric and antisymmetric wave functions? Show that ...

... 6. State and prove Ehernfest’s theorem 7. Solve the Schrodinger equation for a linear harmonic oscillator. Sketch the first two eigenfunctions of the system. 8. Determine the eigenvalue spectrum of angular momentum operators Jz and Jz 9. What are symmetric and antisymmetric wave functions? Show that ...

Lecture 6: 3D Rigid Rotor, Spherical Harmonics, Angular Momentum

... We can now extend the Rigid Rotor problem to a rotation in 3D, corresponding to motion on the surface of a sphere of radius R. The Hamiltonian operator in this case is derived from the Laplacian in spherical polar coordinates given as ...

... We can now extend the Rigid Rotor problem to a rotation in 3D, corresponding to motion on the surface of a sphere of radius R. The Hamiltonian operator in this case is derived from the Laplacian in spherical polar coordinates given as ...

The Hydrogen Atom - Valdosta State University

... Chapter 9 The Hydrogen Atom Goal - to solve for all eigenstates (orbitals) H atom - single nucleus, charge Z (+1) and one eattracted by Coulomb’s Law Will find third quantum number, n, that is ≥ 1 1. Write the full Hamiltonian. Now need to let r ...

... Chapter 9 The Hydrogen Atom Goal - to solve for all eigenstates (orbitals) H atom - single nucleus, charge Z (+1) and one eattracted by Coulomb’s Law Will find third quantum number, n, that is ≥ 1 1. Write the full Hamiltonian. Now need to let r ...

Lecture 01

... We can see that these ladder operators raise or lower the magnetic quantum number m but leave l alone. One can also show that in spherical polar coordinates ...

... We can see that these ladder operators raise or lower the magnetic quantum number m but leave l alone. One can also show that in spherical polar coordinates ...

4.1 Schr¨ odinger Equation in Spherical Coordinates ~

... stationary states 3 Ψn(r, t) = ψn(r)e−iEnt/~, where the spatial wavefunction satisfies the time-independent Schrödinger equation: ~2 ∇ 2 ψ + V ψ = E ψ . − 2m n n n n An arbitrary state can then be written as a sum over these Ψn(r, t). ...

... stationary states 3 Ψn(r, t) = ψn(r)e−iEnt/~, where the spatial wavefunction satisfies the time-independent Schrödinger equation: ~2 ∇ 2 ψ + V ψ = E ψ . − 2m n n n n An arbitrary state can then be written as a sum over these Ψn(r, t). ...

L z

... Thus there exists a common set of eigenfunctions of L2 and Lx And there exists a common set of eigenfunctions of L2 and Ly And there exists a common set of eigenfunctions of L2 and Lz By convention we usually work with the last set of eigenfunctions. NOTE: we can always describe a state which is an ...

... Thus there exists a common set of eigenfunctions of L2 and Lx And there exists a common set of eigenfunctions of L2 and Ly And there exists a common set of eigenfunctions of L2 and Lz By convention we usually work with the last set of eigenfunctions. NOTE: we can always describe a state which is an ...

Physics 214b-2008 Walter F

... However, there will be some extra emphasis on the material since exam 2, since you’ve not yet been tested on that. Material covered since exam 2: Book: Ch. 6 and sections 7.1-7.3, plus appendices B2 and B3.. Assignments: Assignments 10 and 11 Lectures: 27-38 (Friday 4-4-08 through Friday 5-2-08) Equ ...

... However, there will be some extra emphasis on the material since exam 2, since you’ve not yet been tested on that. Material covered since exam 2: Book: Ch. 6 and sections 7.1-7.3, plus appendices B2 and B3.. Assignments: Assignments 10 and 11 Lectures: 27-38 (Friday 4-4-08 through Friday 5-2-08) Equ ...

lect3

... Consider a flux of particles, momentum ħk, energy E= ħ2k2/2m approaching a barrier, height V0 (V0 > E), width a. ...

... Consider a flux of particles, momentum ħk, energy E= ħ2k2/2m approaching a barrier, height V0 (V0 > E), width a. ...

Physics 125b – Problem Set 13 – Due Feb 26,... Version 1 – Feb 21, 2008

... spherical tensor states and operators; Shankar Chapter 15 and Lecture Notes 15. It is clear that the last two weeks have been very rough going for much of the class. Rotations and angular momentum are, in my experience, the toughest part of quantum mechanics because one has to deal with so many fore ...

... spherical tensor states and operators; Shankar Chapter 15 and Lecture Notes 15. It is clear that the last two weeks have been very rough going for much of the class. Rotations and angular momentum are, in my experience, the toughest part of quantum mechanics because one has to deal with so many fore ...

The Addition Theorem for Spherical Harmonics and Monopole

... The key point is to observe that the angular momentum operators in both cases satisfy the same SU(2) algebra. The only difference is that, for ordinary angular momentum operators L, they satisfy ^r:L = 0, where ^r is the radial unit vector. For the monopole angular momentum operators J, we have the ...

... The key point is to observe that the angular momentum operators in both cases satisfy the same SU(2) algebra. The only difference is that, for ordinary angular momentum operators L, they satisfy ^r:L = 0, where ^r is the radial unit vector. For the monopole angular momentum operators J, we have the ...

Chap 6.

... values, ± 12 . The electron is said to be an elementary particle of spin 12 . The proton and neutron also have spin 12 and belong to the classification of particles called fermions, which are govened by the Pauli exclusion principle. Other particles, including the photon, have integer values of spi ...

... values, ± 12 . The electron is said to be an elementary particle of spin 12 . The proton and neutron also have spin 12 and belong to the classification of particles called fermions, which are govened by the Pauli exclusion principle. Other particles, including the photon, have integer values of spi ...

22.101 Applied Nuclear Physics (Fall 2004) Lecture 4 (9/20/04)

... We observe that (4.15) is actually a system of uncoupled equations, one for each fixed value of the orbital angular momentum quantum number l . With reference to the wave equation in one dimension, the extra term involving l(l + 1) in (4.15) represents the contribution to the potential field due to ...

... We observe that (4.15) is actually a system of uncoupled equations, one for each fixed value of the orbital angular momentum quantum number l . With reference to the wave equation in one dimension, the extra term involving l(l + 1) in (4.15) represents the contribution to the potential field due to ...

ANGULAR MOMENTUM So far, we have studied simple models in

... onto z-axis For each eigenvalue of L2, there are (2l+1) eigenfunctions of L2 with the same value of l, but different values of m. Therefore, the degeneracy is (2l+1). The Spherical Harmonic functions are important in the central force problem--in which a particle moves under a force which is due to ...

... onto z-axis For each eigenvalue of L2, there are (2l+1) eigenfunctions of L2 with the same value of l, but different values of m. Therefore, the degeneracy is (2l+1). The Spherical Harmonic functions are important in the central force problem--in which a particle moves under a force which is due to ...

Quantum Mechanics: The Hydrogen Atom

... Recall they are dependent on the principle quantum number only. III. Spectroscopy of the Hydrogen Atom Transitions between the energy states (levels) of individual atoms give rise to characteristic atomic spectra. These spectra can be used as analytical tools to assess composition of matter. For ins ...

... Recall they are dependent on the principle quantum number only. III. Spectroscopy of the Hydrogen Atom Transitions between the energy states (levels) of individual atoms give rise to characteristic atomic spectra. These spectra can be used as analytical tools to assess composition of matter. For ins ...