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10.7: A continuum of quantum states - quantum numbers in a crystal
https://phys.libretexts.org/Bookshelves/Quantum_Mechanics/Quantum_Physics_(Ackland)/10%3A_Self-consistent_field_theory/10.07%3A_A_continuum_of_quantum_states_-_quantum_numbers_in_a_crystal
There are lots of bands crossing the Fermi level, showing that electrons can move from one state to another without requiring energy: potassium is a metal. $\Gamma$ -A is quite a short distance in k-...There are lots of bands crossing the Fermi level, showing that electrons can move from one state to another without requiring energy: potassium is a metal. $\Gamma$ -A is quite a short distance in k-space, corresponding to waves along the long direction in the unit cell: the band structure appears like a parabola “folded back” on itself.
InfoPage
https://phys.libretexts.org/Bookshelves/Quantum_Mechanics/Quantum_Physics_(Ackland)/00%3A_Front_Matter/02%3A_InfoPage
The LibreTexts libraries are Powered by MindTouch ® and are supported by the Department of Education Open Textbook Pilot Project, the UC Davis Office of the Provost, the UC Davis Library, the Californ...The LibreTexts libraries are Powered by MindTouch ® and are supported by the Department of Education Open Textbook Pilot Project, the UC Davis Office of the Provost, the UC Davis Library, the California State University Affordable Learning Solutions Program, and Merlot.
2.5: Notes
https://phys.libretexts.org/Bookshelves/Quantum_Mechanics/Quantum_Physics_(Ackland)/02%3A_Review_-_Time-Independent_Non-degenerate_Perturbation_Theory/2.05%3A_Notes
If the perturbation is turned on and off again, the off-diagonal matrix elements determine whether the quantum state is changed. Similarly, we require that the level shift be small compared to the lev...If the perturbation is turned on and off again, the off-diagonal matrix elements determine whether the quantum state is changed. Similarly, we require that the level shift be small compared to the level spacing in the unperturbed system: However, we need only assume that the particular energy level whose shift we are calculating is non-degenerate for the preceding analysis to be correct. The second order term always lowers the energy of the ground state.
9: Indistinguishable Particles and Exchange
https://phys.libretexts.org/Bookshelves/Quantum_Mechanics/Quantum_Physics_(Ackland)/09%3A_Indistinguishable_Particles_and_Exchange
7: Hydrogen Ion and Covalent Bonding
https://phys.libretexts.org/Bookshelves/Quantum_Mechanics/Quantum_Physics_(Ackland)/07%3A_Hydrogen_ion_and_Covalent_Bonding
7.5: Electronic States of the H₂ Molecule
https://phys.libretexts.org/Bookshelves/Quantum_Mechanics/Quantum_Physics_(Ackland)/07%3A_Hydrogen_ion_and_Covalent_Bonding/7.05%3A_Electronic_states_of_the_H2_Molecule
This must be combined with a spin eigenfunction $\uparrow \uparrow$ , $\downarrow \downarrow$ , $(\uparrow \downarrow + \downarrow \uparrow )$ , or $(\uparrow \downarrow − \downarrow \uparrow )$ ...This must be combined with a spin eigenfunction $\uparrow \uparrow$ , $\downarrow \downarrow$ , $(\uparrow \downarrow + \downarrow \uparrow )$ , or $(\uparrow \downarrow − \downarrow \uparrow )$ , where the first arrow represents the spin state $(m_s = \pm 1)$ of the first electron. $\psi ({\bf r_1},{\bf r_2}, s_1, s_2) = [u^1_{100} ({\bf r_1}) + u^1_{100}({\bf r_2})][u^2_{100}({\bf r_1}) + u^2_{100}({\bf r_2})] [\uparrow \downarrow − \downarrow \uparrow] \nonumber$
16.9: Exercises - Scattering
https://phys.libretexts.org/Bookshelves/Quantum_Mechanics/Quantum_Physics_(Ackland)/16%3A_Exercises/16.09%3A_Exercises_-_Scattering
Given that this is a model for the interaction of light with a fluctuating dipole in a gas molecule, comment on the presence of the factor of $L^3$ in the potential, the angular dependence, the valu...Given that this is a model for the interaction of light with a fluctuating dipole in a gas molecule, comment on the presence of the factor of $L^3$ in the potential, the angular dependence, the values of k’ and the conservation of energy. $\Phi ({\bf r}) = Ae^{i{\bf k}.{\bf r}} + \int G(r−r' )U(r' )Ae^{i{\bf k}.{\bf r}'} d^3 {\bf r}'+ \int G(r−r' )U(r' )G(r'−r'')U(r'')\Phi ({\bf r})d^3 {\bf r}' d^3 {\bf r}'' \nonumber$
10: Self-consistent field theory
https://phys.libretexts.org/Bookshelves/Quantum_Mechanics/Quantum_Physics_(Ackland)/10%3A_Self-consistent_field_theory
An important unsolved problem in quantum mechanics is how to deal with indistinguishable, interacting particles - in particular electrons which determine the behavior of almost every object in nature....An important unsolved problem in quantum mechanics is how to deal with indistinguishable, interacting particles - in particular electrons which determine the behavior of almost every object in nature. The basic problem is that if particles interact, that interaction must be in the Hamiltonian. So until we know where the particles are, we can’t write down the Hamiltonian, but until we know the Hamiltonian, we can’t tell where the particles are.
12.8: General Notes on Scattering in the Born Approximation
https://phys.libretexts.org/Bookshelves/Quantum_Mechanics/Quantum_Physics_(Ackland)/12%3A_Scattering_in_Three_Dimensions/12.08%3A_General_Notes_on_Scattering_in_the_Born_Approximation
The square well illustrates some general feature of scattering in the Born approximation: Thus as energy increases, the scattering angle $\theta$ is reduced and the scattered beam becomes more peake...The square well illustrates some general feature of scattering in the Born approximation: Thus as energy increases, the scattering angle $\theta$ is reduced and the scattered beam becomes more peaked in the ‘straight on’ direction. Angular dependence depends on the range of the potential $a$ but not on the strength $V_0$ . Total cross section depends on both range $a$ and depth $V_0$ of the potential.
9.8: Electron-electron interaction - ground state by perturbation theory
https://phys.libretexts.org/Bookshelves/Quantum_Mechanics/Quantum_Physics_(Ackland)/09%3A_Indistinguishable_Particles_and_Exchange/9.08%3A_Electron-electron_interaction_-_ground_state_by_perturbation_theory
The hydrogen wavefunctions are only a choice of basis set: the hydrogenic potential ignores the electron-electron repulsion. The electron-electron repulsion is over 30% of the unperturbed energy \((4Z...The hydrogen wavefunctions are only a choice of basis set: the hydrogenic potential ignores the electron-electron repulsion. The electron-electron repulsion is over 30% of the unperturbed energy $(4Z\mu e^4/\hbar^2 )$ , so perturbation theory may seem inappropriate. Note also that the radial wavefunctions are different for 2s and 2p, so the electron-electron interation splits the degeneracy between 1s2s and 1s2p configurations.
16.1: Exercises - Mainly revision
https://phys.libretexts.org/Bookshelves/Quantum_Mechanics/Quantum_Physics_(Ackland)/16%3A_Exercises/16.01%3A_Exercises_-_Mainly_revision
(b) Determine the radial distribution function, $D_{10}(r) \equiv r^2 |R_{10}(r)|^2$ , and sketch its behavior; determine the most probable value of the radial coordinate, $r$ , and the probability ...(b) Determine the radial distribution function, $D_{10}(r) \equiv r^2 |R_{10}(r)|^2$ , and sketch its behavior; determine the most probable value of the radial coordinate, $r$ , and the probability that the electron is within a sphere of radius $a_0$ ; recall that $Y_{00}(\theta , \phi ) = 1/ \sqrt{4\pi}$ ; again, you can use Maple to help you if you know how.

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