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, m_s = ±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