The Schrodinger equation in a magnetic field

The spin-less non-relativistic Hamiltonian of interacting particles consists of the kinetic energy and the potential energy 

For a molecule consisting of N nuclei and n electrons exposed to the external electromagnetic field it adopts the form of 

For the electromagnetic field switched off, the Hamiltonian of a free molecule is 

Since p = —i/ V is a differential operator, the product p A should be analysed in more detail, i.e. 

The second term contains the product which can be rewritten as 

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