GATE PH 2013 • Q50
NAT • 2 Marks
Section 2: Classical Mechanics
Classical Mechanics
Subtopic: Lagrangian & Hamiltonian Dynamics & Special Relativity
Question Statement:
The ground state eigenvector of the unperturbed Hamiltonian is
(A) (1/
√2, 1/√2,0 ) (B) (1/ √2, 1/√2,0 ) (C) (0,0,1) (D) (1,0,0)
Step-by-Step Solution & Explanation
### **Official Solution & Step-by-Step Derivation (GATE PH 2013 Q.50)**
**1. Theoretical Formulation & Physics Principles**:
This question examines concepts in **Classical Mechanics** within *Section 2: Classical Mechanics* (2 Marks, 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