Match the following
Column I Column II (P) Associated Legendre polynomials (III) Angular part of H atom (Q) Hermite polynomials (I) Harmonic oscillator (R) Associated Laguerre polynomials (IV) Radial part of H atom (S) Trigonometric functions (II) Particle in a box model
Match the following
| Column I | Column II |
|---|---|
| (P) Associated Legendre polynomials | (III) Angular part of H atom |
| (Q) Hermite polynomials | (I) Harmonic oscillator |
| (R) Associated Laguerre polynomials | (IV) Radial part of H atom |
| (S) Trigonometric functions | (II) Particle in a box model |
Show Hint
Harmonic oscillator: Hermite polynomials.
Particle in a box: Sine and cosine (trigonometric).
- P→III, Q→I, R→IV, S→II
- P→III, Q→IV, R→II, S→I
- P→IV, Q→I, R→III, S→II
- P→II, Q→III, R→IV, S→I
The Correct Option is A
Solution and Explanation
- The angular part of the hydrogen atom wavefunction (spherical harmonics) involves Associated Legendre polynomials.
- The harmonic oscillator solutions are expressed in terms of Hermite polynomials.
- The radial part of the hydrogen atom wavefunction involves Associated Laguerre polynomials.
- The particle in a box has solutions in terms of trigonometric functions (sine and cosine).
Step 2: Match each entry.
- \(P \to III\): Associated Legendre polynomials → angular part of H atom.
- \(Q \to I\): Hermite polynomials → harmonic oscillator.
- \(R \to IV\): Associated Laguerre polynomials → radial part of H atom.
- \(S \to II\): Trigonometric functions → particle in a box.
\[ \boxed{\text{P→III, Q→I, R→IV, S→II = Option (A)}} \]
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