# Chemistry 3451 (Physical Chemistry III) ```Chemistry 3451 (Physical Chemistry III) Information Sheet Dimensions, Physical Constants, Conversion Factors and other useful information Dimensions: Page 2 of 31
Physical Constants: Useful Conversion Factors: Page 3 of 31
Useful Prefixes for Powers of Ten: The Greek Alphabet: Page 4 of 31
Integrals: Useful Mathematical Topics (Integrals, Derivative Properties, Imaginary numbers and Relationships) Page 5 of 31
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Some Calculus Rules: Differential Equations: Second order differential equations have two solutions Page 9 of 31
Hermite’s Differential Equation (associated) Legendre’s Differential Equation for m &lt; 0 Separation of Variables Assumed, without initial justification, that the dependent variable can be written as a product now can be decomposed into two ordinary differential equations and solve Page 10 of 31
Trigonometry: Page 11 of 31
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Complex Numbers: ; ; ; ; Page 13 of 31
Vectors and Matrices: Vectors are ordered N-&shy;‐tuples of numbers dot-&shy;‐ or inner-&shy;‐product (scalar) norm (or generalized length) matrix is a square N x N array Unit Matrix Multiplication of a vector by a matrix on the left gives a new vector the product of two matrices is a matrix The transpose of a matrix is given by
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the adjoint (or Hermitian conjugate) is given by The determinant of a matrix the expectation value in matrix form The eigenvalue problem in matrix formulation the cross-&shy;‐product (a new matrix of size N x M) Page 15 of 31
Some useful identities involving scalar and cross-&shy;‐products Angular Momentum: Bra-&shy;‐Ket notation: Page 16 of 31
More Useful Relationships: The Taylor Series Expansion of a (well-&shy;‐behaved) function f(x) about the point x=a: where The gradient-&shy;‐squared (or Laplacian) operator in Cartesian, Polar and Spherical-&shy;‐Polar coordinates: Page 17 of 31
Group Theory Flow Scheme for Group Symbols: Character Tables: Page 18 of 31
Special, High Symmetry Groups
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Groups with no axis of symmetry
The S2n Groups
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The Cn Groups
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The Cnv Groups
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The Cnh Groups
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The Dn Groups
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The Dnd Groups
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The Dnh Groups
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