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ฟิสิกส์โอลิมปิก วิทยาศาสตร์โอลิมปิก ข้อสอบแข่งขัน ข้อสอบชิงทุน => GRE - Physics => Topic started by: conantee on December 08, 2010, 04:59:31 AM



Title: GR9677.100
Post by: conantee on December 08, 2010, 04:59:31 AM
100. The operator \hat{a} = \sqrt{\frac{m\omega_0}{2\hbar}}(\hat{x} + i\frac{\hat{p}}{m\omega_0}), when operating on a harmonic energy eigenstate \Psi_n with energy E_n, produces another energy eigenstate whose energy is E_n - \hbar \omega_0. Which of the following is true?
I. \hat{a} commutes with the Hamiltonian.
II. \hat{a} is a Hermitian operator and therefore an observable.
III. The adjoint operator\hat{a}^\dagger \neq \hat{a}.

(A) I only
(B) II only
(C) III only
(D) I and II only
(E) I and III only