Quantum Mechanics in Matrix Form by Günter Ludyk

Author:Günter Ludyk
Language: eng
Format: epub, pdf
Publisher: Springer International Publishing, Cham

where is an arbitrary three-dimensional vector. In the case of the Heisenberg matrices of the matrix vector

the equivalent condition is

or

In other words, we are looking for a unitary matrix such that

(8.5)

For infinitesimally small , must have a shape like that in (8.1). Therefore, it seems useful to start with the ansatz

(8.6)

The dimension of is . It turns out later that represents the momentum (with dimension ) and that the have the dimension length. It is therefore convenient to add the in order to render a dimensionless transformation matrix. For an infinitesimal three-vector the condition (8.5) requires that

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