User:Benjah-bmm27/degree/2/FRM

Quantum mechanics, FRM
"Quantum Concepts"
 * Molecular structure
 * Reactivity
 * Quantum chemistry
 * Nuclei much heavier than electrons ∴ molecules have structure
 * Electrostatics, internuclear repulsion
 * Zero-point energy
 * Born-Oppenheimer approximation
 * Potential energy surfaces: minima correspond to stable structures, saddle points correspond to transition states, reaction pathways correspond to mechanisms
 * Conformation of ethane, nitrogen inversion
 * de Broglie wavelength
 * Schrödinger equation
 * Hamiltonian operator
 * Wavefunctions
 * Particle in a box
 * Boundary conditions
 * Heisenberg uncertainty principle
 * Hydrogen atom
 * Spherical polar coordinates
 * Electron spin: Stern-Gerlach experiment suggested electrons have intrinsic, quantized spin angular momentum. It is now known that the spin angular momentum quantum number s = ½, and the spin projection quantum number, ms = ±½.
 * Molecular Schrödinger equation
 * Molecular orbital approximation, molecular orbital theory (ignores electronic correlation)
 * Normalization of wavefunctions
 * Orthogonality: In quantum mechanics, two eigenstates of a wavefunction, $$ \psi_m $$ and $$ \psi_n $$, are orthogonal if they correspond to different eigenvalues. This means, in Dirac notation, that $$ \langle \psi_m | \psi_n \rangle = 0 $$ unless $$ \psi_m $$ and $$ \psi_n $$ correspond to the same eigenvalue. This follows from the fact that Schrödinger's equation is a Sturm–Liouville equation (in Schrödinger's formulation) or that observables are given by hermitian operators (in Heisenberg's formulation).
 * Expectation value (quantum mechanics): $$\left\langle {\hat \Omega } \right\rangle = \int {\psi ^ *  \hat \Omega \psi } {\text{ d}}\tau$$
 * Variational principle
 * Linear combination of atomic orbitals molecular orbital method
 * Vibrational spectroscopy: molecular vibration, harmonic approximation cf. classical oscillator
 * Quantum tunnelling
 * Kinetic isotope effect, e.g. in amine dehydrogenase
 * Reaction coordinate
 * Transition state theory
 * Morse potential