Dielectric, Magnetic Properties & Superconductivity
Subtopic: Meissner Effect, Type I and Type II Superconductors
Question Statement:
Three non-interacting bosonic particles of mass m each, are in a one-
dimensional infinite potential well of width a. The energy of the third excited
state of the system is xx him?
ma?. The value of x (in integer) is -
Official Answer Key:
5 to 6
Step-by-Step Solution & Explanation
### **Official Solution & Step-by-Step Derivation (GATE PH 2021 Q.31 / PH Q.21)**
**1. Physical Principles & Examination Context**:
- **Topic**: *Dielectric, Magnetic Properties & Superconductivity* (`Meissner Effect, Type I and Type II Superconductors`) | **Section**: *Section 7: Solid State Physics*
- **Question Type**: **NAT** | **Marks**: **1 Mark** | **Negative Marks**: **0**
- **Governing Principles**: Solved directly by applying fundamental laws of **Dielectric, Magnetic Properties & Superconductivity**.
**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 **5 to 6**.
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