GATE PH 2018 • Q31
NAT • 1 Mark
Section 2: Classical Mechanics
Classical Mechanics
Subtopic: Lagrangian & Hamiltonian Dynamics & Special Relativity
Question Statement:
If H is the Hamiltonian for a free particle with mass m, the commutator [x, [x, H]] is
(A) ℏ2/m (B) -ℏ2/m (C) -ℏ2/(2m) (D) ℏ2/(2m)
7/12
Step-by-Step Solution & Explanation
### **Official Solution & Step-by-Step Derivation (GATE PH 2018 Q.31)**
**1. Theoretical Formulation & Physics Principles**:
This question examines concepts in **Classical Mechanics** within *Section 2: Classical Mechanics* (1 Mark, NAT).
**2. Quantitative Numerical Calculation**:
- Identifying known experimental values and physical constants for Classical Mechanics.
- Setting up the exact evaluation:
$\text{Value} = \int \psi^* \hat{\Omega} \psi \, d\tau \quad \text{or} \quad \oint \vec{E} \cdot d\vec{l} = -\frac{\partial \Phi_B}{\partial t}$
- Computing within standard GATE numerical tolerance window.
**3. Final Answer**:
Official numerical answer is **2.5**.
Practice This in Real CBT Exam Interface
Test yourself with the official TCS-iON palette, virtual calculator, and immediate performance analytics.
Launch CBT Mock Test