A two-dimensional square lattice has lattice constant a.
k represents the wavevector in reciprocal space. The coordinates (kx, ky)
of reciprocal space where band gap(s) can occur, are
(A)
(0,0)
(B)
(+*+3)
(+3)
@ (+3+3)
Options:
(A) (0,0)
(B) (+*+3) (+3) @ (+3+3)
Official Answer Key:
B, C, D
Step-by-Step Solution & Explanation
### **Official Solution & Step-by-Step Derivation (GATE PH 2021 Q.20 / PH Q.10)**
**1. Physical Principles & Examination Context**:
- **Topic**: *Schrodinger equation & Wave Mechanics* (`1D Potential Wells, Steps & Tunneling`) | **Section**: *Section 4: Quantum Mechanics*
- **Question Type**: **MSQ** | **Marks**: **1 Mark** | **Negative Marks**: **0**
- **Governing Principles**: Solved directly by applying fundamental laws of **Schrodinger equation & Wave Mechanics**.
**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 **B, C, D**.
Practice This in Real CBT Exam Interface
Test yourself with the official TCS-iON palette, virtual calculator, and immediate performance analytics.