formula sheet w07 - 2(11 Liouville-von Neumann equation...

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1 Formula Sheet ( Chem113A W’07 ) Need more equations/constants? Just raise your hand during the self evaluations. (1) Definition of adjoint operator (2) Definition of Hermitian operator: A + = A . (3) Adjoint operator algebra For an arbitrary scalar c and arbitrary operators A and B : (a) ( A + B ) + = A + + B + ;(b) ( AB ) + = B + A + ; (c) ( c A ) + = c * A + ; (d) ( A + ) + = A . (4) Commutator algebra (5) Dirac bracket notation: (6) Dirac algebra for quantum HO (in the reduced units): [ x , p ] = i , a = 2 i ( p i x ), a + = 2 1 i ( p + i x ) . (7) Schrodinger Representation: x x , x i p p h (8) Schrodinger equation: Time-dependent: d| Ψ (t)>/dt = (-i/ ħ ) H| Ψ (t)> ; time-independent: H| Ψ >=E|| Ψ > (9) Erhenfest equation: equation of motion for the expectation value (10) Heisenberg equation: equation of motion for the Heisenberg operator
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Unformatted text preview: 2 (11) Liouville-von Neumann equation: equation of motion for the density operator (12) Quantum simple harmonic oscillators: (13) Recursive relations for Hermite polynominal Hn (14) Particle in a 1D box: , (15) 2-Body -> 1-Body transformation: (16) Classical Poisson bracket: (17) Hamilton’s equation (master equation for the Hamiltonian mechanics): (18) Dirac’s quantum condition: 3 (19) QM Postulates: (20) Integral formula: 4 (21) Physical constants: (22) Quantum mechanical operators: 5 (23) Conversion factors: (24) Periodic table: (25) Spherical coordinate system...
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