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Indian Forest Service (Mains)

Chemistry optional

  • 2 papers
  • 200 marks each
  • 3 h per paper

Paper I covers physical and inorganic chemistry.

Indian Forest Service (Mains), Chemistry optional · 2021 · Paper I

Q2(a). Particle in a one-dimensional box

Question

Prove that for a particle in the box, the total energy eigenfunctions are φₙ(x) = √(2/L) sin(nπx/L), where φ(x) is a continuous function at the edges of the box. Is dφ(x)/dx a continuous function of x at the edges of the box? The dimensions of the box are from x = 0 to x = L.

Answer in brief

For an infinite box, φₙ = √(2/L) sin(nπx/L) and Eₙ = n²h²/(8mL²); the wavefunction is continuous, but its first derivative jumps at the infinite walls.

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Read the whole 2021 solution2021 question paper

Coversparticle in a one-dimensional boxboundary conditionswavefunction continuitynormalisationenergy eigenvalues

All parts of Question 2