Tiêu đề QM DPP Sheet 09.pdf ✅

1 North Delhi : 56-58, First Floor, Mall Road, G.T.B. Nagar (Near Metro Gate No. 3), Delhi-09, Ph: 011-41420035 South Delhi : 28-A/11, Jia Sarai, Near-IIT Metro Station, New Delhi-16, Ph : 011-26851008, 26861009 IIT JAM PHYSICS 2024 Section: MODERN PHYSICS (Quantum Mechanics) Chapter: OPERATOR FORMALISM - II Daily Practice Problem (DPP) Sheet 9 1. The value of the commutator bracket 2 2 ˆ , ˆ x x p    (where xˆ and ˆ x p are position and linear momentum operators respectively) is (a) 2i xp   ˆˆ x  p x ˆ ˆ x  (b) 2i xp   ˆˆ x  p x ˆ ˆ x  (c) 4 ˆˆ x i xp  (d) 4 ˆ ˆ x i p x  2. The value of the commutator bracket ˆ x x H ˆ, ˆ,       (where xˆ and Hˆ are position and Hamiltonian operators respectively) is (a) 2 i m  (b) 2 i m   (c) 2 m   (d) 2 m  3. The value of the commutator bracket   ˆ , F x x        is (a)   F x ˆ (b) ˆ I (c) - ˆ I (d) Fˆ x   4. Let xˆ and ˆ x p denote the coordinate and momentum operators satisfying the canonical commutation relation  x p ˆ ˆ , x   i in natural units  1. Then the commutator  xˆ,sin pˆ x  is (a) cos ˆ x i p (b) cos ˆ x i p (c) sin ˆ x i p (d) sin ˆ x i p 5. The value of the commutator brackets  xpˆˆ x  p x p ˆ ˆ ˆ x , x  and  xpˆˆ x  p x x ˆ ˆ ˆ x ,  (where xˆ and ˆ x p are position and linear momentum operators respectively) are (a) 2 ˆ , 2 ˆ x i p  i x (b) 2 ˆ , 2 ˆ x i p i x (c) 2 ˆ , 2 ˆ x  i p i x (d) 2 ˆ , 2 ˆ x  i p  i x 6. The value of the commutator bracket 2 2 ˆ xˆ, x         is (a) ˆ 2 x    (b) ˆ 2 x   (c) ˆ x    (d) ˆ x  