Consider a spinS - /z particle in the state lp) - 117 . The probability
that a measurement finds the state with Sx = +h/2 is
(A) | 5/18
(B) | 11/18
(C) | 15/18
(D) 17/18
Options:
(A) | 5/18
(B) | 11/18
(C) | 15/18
(D) 17/18
Official Answer Key:
D
Step-by-Step Solution & Explanation
### **Official Solution & Step-by-Step Derivation (GATE PH 2021 Q.38 / PH Q.28)**
**1. Physical Principles & Examination Context**:
- **Topic**: *Fourier and Laplace transforms* (`Fourier Series & Integral Transforms`) | **Section**: *Section 1: Mathematical Physics*
- **Question Type**: **MCQ** | **Marks**: **2 Marks** | **Negative Marks**: **0.67**
- **Governing Principles**: Solved directly by applying fundamental laws of **Fourier and Laplace transforms**.
**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 **D**.
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