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hy do we call a as annihilation operator and â as creation operator, i.e. what is the physical meaning of them? (596) 6. W

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The names Annihilation operator and creation operators are taken from the quantum treatment of light. Annihilation operator and creation operators are called Ladder operators.

The creation operator create one quantum of energy and annihilation operators annihilate one quantum of energy. Therefore, the creation operator is also called as raising operator and annihilation operator is called lowering operator.

Example: In the case of an Harmonic oscillatot If a quantum energy state f with energy E then the total energy (halmiltonian) can be expressed as This implies that afe is an eigen function of H with energy, (E-ha Thus a is called lowering operator For the same calculations, al instead a, we get a% 1s an eigen state and energy E+ha Thus, a is called lowering operator

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