(A)
A matter wave is represented by the wave function
Ф(x, y, z, t) = Aei (4x+3y+52-10mt)
where A is a constant. The unit vector representing the direction of
propagation of this matter wave is
3
5V2 + F2
(B)
5V2
(C)
(D)
1
5VZ
4
5VZ
Options:
(A) A matter wave is represented by the wave function Ф(x, y, z, t) = Aei (4x+3y+52-10mt) where A is a constant. The unit vector representing the direction of propagation of this matter wave is 3 5V2 + F2
(B) 5V2
(C)
(D) 1 5VZ 4 5VZ
Official Answer Key:
A
Step-by-Step Solution & Explanation
### **Official Solution & Step-by-Step Derivation (GATE PH 2021 Q.12 / PH Q.2)**
**1. Physical Principles & Examination Context**:
- **Topic**: *Complex analysis* (`Residue Theorem & Contour Integration`) | **Section**: *Section 1: Mathematical Physics*
- **Question Type**: **MCQ** | **Marks**: **1 Mark** | **Negative Marks**: **0.33**
- **Governing Principles**: Solved directly by applying fundamental laws of **Complex analysis**.
**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 **A**.
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