Hermite, Charles

Herman R.M., 274 Hermite Charles, 191 Herschbach Dudley R., 161, 212, 589, 707, 886 Hertz Gustav, 302 Herzberg Gerhard 259,... 

Note that a symmetric matrix is unchanged by rotation about its principal diagonal. The complex-number analogue of a symmetric matrix is a Hermitian matrix (after the mathematician Charles Hermite) this has atJ = a, e.g. if element (2,3) = a + bi, then element (3,2) = a — bi, the complex conjugate of element (2,3) i = f 1. Since all the matrices we will use are real rather than complex, attention has been focussed on real matrices here. 

Charles Hermite was a French mathematician (1822-1901), professor of Sorhonne. The Hermite polynomials were defined half a century earlier hy Pierre Laplace. 

Equation (7.6) must hold for every function that can represent a possible state of the system that is, it must hold for all well-behaved functions A linear operator that satisfies (7.6) for all well-behaved functions is called a Hermitian operator (after the mathematician Charles Hermite). 

It turns out that the set of harmonic oscillator wavefunctions were already known. This is because differential equations like those of equation 11.6, the rewritten Schrodinger equation, had been studied and solved mathematically before quantum mechanics was developed. The polynomial parts of the harmonic oscillator wavefunctions are called Hermite polynomials after Charles Hermite, the nineteenth-century French mathematician who studied their properties. For convenience, if we define (where is the Greek letter xi, pronounced... 

This property is named for Charles Hermite (1822-1901), a famous French mathematician. 

The Hermite equation Is named for Charles Hermite, 1822-1901, a great French mathematician who made many contributions to mathematics, Including the proof that e (2.71828...) Is a transcendental irrational number. 

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