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steve9983
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How do you find the hermitian conjugate of x, i, d()/d(x), a+ 'the harmonic oscilator raising operator'?
How do you find the hermitian conjugate of x,
i,
d()/d(x),
a+
luke said:Maybe I am missing something obvious but how do you show that x is hermitian
A Hermitian conjugate is a mathematical operation that involves taking the complex conjugate of a quantity and then transposing it. In other words, it involves changing the sign of the imaginary component and switching the rows and columns of a matrix.
The Hermitian conjugate of x is simply the complex conjugate of x, denoted by x*, since x is a real number and has no imaginary component.
The Hermitian conjugate of i is -i, since the complex conjugate of i is -i and there is no transposition necessary for a single number.
The Hermitian conjugate of d/dx is -d/dx, since the complex conjugate of d/dx is -d/dx and there is no transposition necessary for a single operator.
The Hermitian conjugate of a+ is the complex conjugate of a, denoted by a*, since a is a constant and has no imaginary component. The + sign is simply dropped as it represents the adjoint operator in quantum mechanics.