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- https://phys.libretexts.org/Bookshelves/Quantum_Mechanics/Advanced_Quantum_Mechanics_(Kok)/zz%3A_Back_Matter/10%3A_Index
- https://phys.libretexts.org/Bookshelves/Quantum_Mechanics/Advanced_Quantum_Mechanics_(Kok)/05%3A_Composite_Systems_and_Entanglement
- https://phys.libretexts.org/Bookshelves/Quantum_Mechanics/Advanced_Quantum_Mechanics_(Kok)/00%3A_Front_Matter/02%3A_InfoPageThe 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.
- https://phys.libretexts.org/Bookshelves/Quantum_Mechanics/Advanced_Quantum_Mechanics_(Kok)/09%3A_New_PageIn this final section we study a variety of problems in many-body quantum mechanics. First, we introduce the Hartree-Fock method for taking into account the effect of electron-electron interactions in...In this final section we study a variety of problems in many-body quantum mechanics. First, we introduce the Hartree-Fock method for taking into account the effect of electron-electron interactions in atoms. Next, we describe spin waves in magnetic materials using the Heisenberg model. Third, we describe the behaviour of an atom interacting with photons in a cavity, and introduce the Jaynes-Cummings Hamiltonian. And finally, we take a brief look at the basic ideas behind quantum field theory.
- https://phys.libretexts.org/Bookshelves/Quantum_Mechanics/Advanced_Quantum_Mechanics_(Kok)/14%3A_Atomic_Orbitals/14.2%3A_The_OrbitalsIn a single-electron atom, to first order the energy of the atom is determined entirely by n. (There are second order effects, such as the magnetic interaction between the spin and orbit of the el...In a single-electron atom, to first order the energy of the atom is determined entirely by n. (There are second order effects, such as the magnetic interaction between the spin and orbit of the electron, that are beyond the scope of this class.) The ground state has n=1, and higher shells have larger values of n.
- https://phys.libretexts.org/Bookshelves/Quantum_Mechanics/Advanced_Quantum_Mechanics_(Kok)/12%3A_Multiple_Particle_States/12.4%3A_Fermions_and_Bosons\hat{P}_{12}|\xi\rangle &=\hat{P}_{12}\left(\frac{1}{\sqrt{2}}\left|+z_{1}\right\rangle\left|-z_{2}\right\rangle-\frac{1}{\sqrt{2}}\left|+z_{2}\right\rangle\left|-z_{1}\right\rangle\right) \\ &=\frac{...\hat{P}_{12}|\xi\rangle &=\hat{P}_{12}\left(\frac{1}{\sqrt{2}}\left|+z_{1}\right\rangle\left|-z_{2}\right\rangle-\frac{1}{\sqrt{2}}\left|+z_{2}\right\rangle\left|-z_{1}\right\rangle\right) \\ &=\frac{1}{\sqrt{2}} \hat{P}_{12}\left|+z_{1}\right\rangle\left|-z_{2}\right\rangle-\frac{2}{\sqrt{2}} \hat{P}_{12}\left|+z_{2}\right\rangle\left|-z_{1}\right\rangle \\
- https://phys.libretexts.org/Bookshelves/Quantum_Mechanics/Advanced_Quantum_Mechanics_(Kok)/03%3A_Schrodinger_and_Heisenberg_Pictures\[\frac{d}{d t} \operatorname{Tr}\left[\left|\psi_{S}(t)\right\rangle\left\langle\psi_{S}(t)\right| A_{S}\right]=\frac{d}{d t}\left\langle\psi_{S}(t)\left|A_{S}\right| \psi_{S}(t)\right\rangle=\frac{d...ddtTr[|ψS(t)⟩⟨ψS(t)|AS]=ddt⟨ψS(t)|AS|ψS(t)⟩=ddt⟨ψH|AH(t)|ψH⟩ Using |ψ(t)⟩I=U†0(t)|ψ(t)⟩S with U0(t)=exp(−iH0t/ℏ), calculate the time dependence of an operator in the interaction picture AI(t).
- https://phys.libretexts.org/Bookshelves/Quantum_Mechanics/Advanced_Quantum_Mechanics_(Kok)/16%3A_MatterWe’ve concentrated primarily on electrons throughout this course. Indeed, in our everyday life, it is the interactions of electrons that, together with photons (light), drive most of what we do. In th...We’ve concentrated primarily on electrons throughout this course. Indeed, in our everyday life, it is the interactions of electrons that, together with photons (light), drive most of what we do. In this final chapter, we’ll peer down inside the atom to see what the most fundamental particles are, and then extend our view out to bulk states comprised of large numbers of electrons.
- https://phys.libretexts.org/Bookshelves/Quantum_Mechanics/Advanced_Quantum_Mechanics_(Kok)/12%3A_Multiple_Particle_States/12.1%3A_Indistinguishable_ParticlesThis means that if you have a state with two electrons, you can swap the two electrons and it cannot change anything physically observable from that state. Then, the expectation value of any operator ...This means that if you have a state with two electrons, you can swap the two electrons and it cannot change anything physically observable from that state. Then, the expectation value of any operator must be the same for these two different states: Also, the probability for any measurement of any observable to be made must be the same for the two states. Below, we will introduce the exchange operator as a way of quantifying the effect of identical particles on quantum states.
- https://phys.libretexts.org/Bookshelves/Quantum_Mechanics/Advanced_Quantum_Mechanics_(Kok)/13%3A_The_Schrodinger_Equation/13.1%3A_Where_we_are_so_farA state that is a definite state for a given observable is an eigenstate of that operator. (We would also say that the ket vector that represents that state is an eigenvector of the operator; if we’re...A state that is a definite state for a given observable is an eigenstate of that operator. (We would also say that the ket vector that represents that state is an eigenvector of the operator; if we’re representing operators as matrices, then the column vector that represents the state is an eigenvector of the operator.) An operator working on one of its eigenstate returns a constant times the same state.
- https://phys.libretexts.org/Bookshelves/Quantum_Mechanics/Advanced_Quantum_Mechanics_(Kok)/05%3A_Composite_Systems_and_Entanglement/5.03%3A_Quantum_teleportation|\chi\rangle=& \frac{1}{2}\left[\alpha\left|\Phi^{+}\right\rangle_{12}|0\rangle_{3}+\alpha\left|\Phi^{-}\right\rangle_{12}|0\rangle_{3}+\alpha\left|\Psi^{+}\right\rangle_{12}|1\rangle_{3}+\alpha\left|...|\chi\rangle=& \frac{1}{2}\left[\alpha\left|\Phi^{+}\right\rangle_{12}|0\rangle_{3}+\alpha\left|\Phi^{-}\right\rangle_{12}|0\rangle_{3}+\alpha\left|\Psi^{+}\right\rangle_{12}|1\rangle_{3}+\alpha\left|\Psi^{-}\right\rangle_{12}|1\rangle_{3}\right.\\ &\left.+\beta\left|\Psi^{+}\right\rangle_{12}|0\rangle_{3}-\beta\left|\Psi^{-}\right\rangle_{12}|0\rangle_{3}+\beta\left|\Phi^{+}\right\rangle_{12}|1\rangle_{3}-\beta\left|\Phi^{-}\right\rangle_{12}|1\rangle_{3}\right] \\
