Lecture 9: The Harmonic Oscillator: Creation and Annihilation Operators | Physical Chemistry | Chemistry | MIT OpenCourseWare

(a) The quantum harmonic oscillator Hamiltonian can be written in terms of creation and annihilation operators as:H = (1/2m) * (a^2 a^2)(i) Given [a, a^ ] = 1, use the above expression for H in terms of the annihilation and creation operators to show that [a, H] = hw*a.(ii) Explain why the ground state |0> is characterized by the condition a|0> = 0.(iii) Deduce the energy eigenvalue of the ground state.(b) Suppose that the operators b and b^ obey the anti-commutation relation b, b^ = bb^

Creation and annihilation operators acting on energy eigenstates | Quantum Physics I | Physics | MIT OpenCourseWare