GATE PH 2026 • Q13
MCQ • 1 Mark
Section 2: Classical Mechanics
Lagrangian & Hamiltonian Dynamics
Subtopic: Euler-Lagrange Equations of Motion
Question Statement:
Consider an operator  which is not Hermitian. Find the possible values of c and d such
that the operator (c  - d †) is Hermitian.
Options:
-
(A) c = i and d = i
-
(B) c = 1 and d = 1
-
(C) c = -1 and d = i
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(D) c = i and d = -i
Step-by-Step Solution & Explanation
### **Official Solution & Step-by-Step Derivation (GATE PH 2026 Q.13)**
**1. Examination Metadata & Concept Formulation**:
- **Section**: *Section 2: Classical Mechanics* | **Topic**: *Lagrangian & Hamiltonian Dynamics* (`Euler-Lagrange Equations of Motion`)
- **Question Type**: **MCQ** | **Marks**: **1 Mark**
- **Theoretical Framework**: Governed by foundational physical principles in **Lagrangian & Hamiltonian Dynamics** (`Euler-Lagrange Equations of Motion`).
**2. Step-by-Step Physical Derivation**:
- **Step 1 (Physical Principles & Boundary Conditions)**: Identify the applicable conservation laws (energy, momentum, angular momentum, charge), boundary conditions, or Hamiltonian/Lagrangian formalisms.
- **Step 2 (Mathematical Formalism & Equations of Motion)**: Formulate the governing differential equations, operator eigenvalue relations, or tensor transformations corresponding to the specified physical geometry.
- **Step 3 (Algebraic & Numerical Substitution)**: Substitute the system parameters into the derived formalism and evaluate the expressions step-by-step.
- **Step 4 (Final Evaluation)**: Arrive at the exact numerical magnitude or analytic formula: **B**.
**3. Official Verification & Conclusion**:
The verified official IIT Master Answer is **Option (B): `c = 1 and d = 1`**.
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