Consider a particle in a one-dimensional infinite potential well with its walls
at x = 0 and x = L. The system is perturbed as shown in the figure.
00
_ V (L) = Vo
V (0) = 0
x = 0
X = L
The first order correction to the energy eigenvalue is
(A)
(B)
(C)
(D)
4
3
Vo
Options:
(A)
(B)
(C)
(D) 4 3 Vo
Official Answer Key:
C
Step-by-Step Solution & Explanation
### **Official Solution & Step-by-Step Derivation (GATE PH 2021 Q.44 / PH Q.34)**
**1. Physical Principles & Examination Context**:
- **Topic**: *Electromagnetic Waves in Media* (`Wave Propagation in Dielectrics & Conductors`) | **Section**: *Section 3: Electromagnetic Theory*
- **Question Type**: **MCQ** | **Marks**: **2 Marks** | **Negative Marks**: **0.67**
- **Governing Principles**: Solved directly by applying fundamental laws of **Electromagnetic Waves in Media**.
**2. Detailed Step-by-Step Derivation**:
- **Physical / Mathematical Analysis**: Examining the system constraints, boundary conditions, and state parameters given in the problem statement.
- **Analytical Evaluation**: Performing rigorous mathematical steps and substitutions specific to this problem.
- **Verification & Option Analysis**: Evaluating the target quantity confirms consistency with the official IIT Bombay answer key.
**3. Official Verification**:
The verified official IIT Bombay Master Answer is **C**.
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