If a and b are constant vectors, & and p are generalized positions and
conjugate momenta, respectively, then for the transformation @ = a p and
P = b \cdotF to be canonical, the value of & \cdot b (in integer) is _
Official Answer Key:
-1 to -1
Step-by-Step Solution & Explanation
### **Official Solution & Step-by-Step Derivation (GATE PH 2021 Q.35 / PH Q.25)**
**1. Physical Principles & Examination Context**:
- **Topic**: *Nuclear Models & Decays* (`Nuclear Shell Model & Magic Numbers`) | **Section**: *Section 9: Nuclear and Particle Physics*
- **Question Type**: **NAT** | **Marks**: **1 Mark** | **Negative Marks**: **0**
- **Governing Principles**: Solved directly by applying fundamental laws of **Nuclear Models & Decays**.
**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 **-1 to -1**.
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