he momentum operator as a vector

# he momentum operator as a vector - (11.3 where the square...

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he momentum operator as a vector First of all we know from classical mechanics that velocity and momentum, as well as position, are represented by vectors. Thus we need to represent the momentum operator by a vector of operators as well, (11.1) There exists a special notation for the vector of partial derivatives, which is usually called the gradient, and one writes (11.2) We now that the energy, and Hamiltonian, can be written in classical mechanics as
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Unformatted text preview: (11.3) where the square of a vector is defined as the sum of the squares of the components, (11.4) The Hamiltonian operator in quantum mechanics can now be read of from the classical one, (11.5) Let me introduce one more piece of notation: the square of the gradient operator is called the Laplacian, and is denoted by ....
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