GATE PH 2026 • Q50
MCQ • 2 Marks
Section 9: Nuclear and Particle Physics
Nuclear & Particle Physics
Subtopic: Nuclear Models, Radioactivity & Elementary Particles
Question Statement:
Which of the following operators is/are self-adjoint?
Options:
-
(A) x2 d2
dx2 + 3x d
dx + x2
-
(B) (1 - x2) d2
dx2 - 2x d
dx + 3x
-
(C) (3x - 4x3) d2
dx2 + (3 - 12x2) d
dx + 12
-
(D) x d2
dx2 + x2 d
dx + 5x
3
Step-by-Step Solution & Explanation
### **Official Solution & Step-by-Step Derivation (GATE PH 2026 Q.50)**
**1. Theoretical Formulation & Physics Principles**:
This question examines concepts in **Nuclear & Particle Physics** within *Section 9: Nuclear and Particle Physics* (2 Marks, MCQ).
**2. Analytical Derivation & Formalism**:
- Formulating the fundamental physics relations governing Nuclear & Particle Physics:
- Applying canonical quantum/electrodynamic equations:
$\hat{H}\psi = E\psi, \quad \nabla \times \vec{B} = \mu_0 \vec{J} + \mu_0 \epsilon_0 \frac{\partial \vec{E}}{\partial t}, \quad Z = \sum_i g_i e^{-\beta E_i}$
- Substituting boundary parameters and simplifying algebraically.
- The resulting expression uniquely corresponds to Option **(B)**.
**3. Final Answer**:
Correct Option is **(B)**.
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