momentum operator उदाहरण वाक्य

The energy and momentum operators are " differential operators ", while the potential energy function is just a multiplicative factor.
For a single particle with no electric charge and no spin, the momentum operator can be written in the position basis as:
Creation and annihilation operators can be constructed for spin-objects; these obey the same commutation relations as other angular momentum operators.
The left side represents the square of the momentum operator divided by twice the mass, which is the non-relativistic kinetic energy.
Informally stated, with certain technical assumptions, every representation of the Heisenberg group is equivalent to the position operators and momentum operators on.

Also, since the momentum operator is unitarily equivalent to the position operator, via the Fourier transform, they have the same spectrum.
The derivative operators, and hence the energy and 3-momentum operators, are also non-invariant and change under Lorentz transformations.
This can be proven in a similar way as the above, but using the fact that translation operators commute with the momentum operator.
The relationship between the angular momentum operator and the rotation operators is the same as the relationship between lie algebras and lie groups in mathematics.
(In practice, when working through this math, we usually apply angular momentum operators to the states, rather than rotating the states.