Q4(c). Schrödinger wave equation in three dimensions; meaning of ψ and ψ²
Set up the Schrödinger wave equation (three dimensions). Comment on the nature of the equation and various terms involved. Explain the significance of ψ and ψ².
Answer in brief
(∂²ψ)/(∂ x²)+(∂²ψ)/(∂ y²)+(∂²ψ)/(∂ z²)+(8π²m)/(h²)(E-V)ψ=0, or Hψ=Eψ: a linear, second-order partial differential (eigenvalue) equation. ψ is the amplitude function that describes the state; ψ² dτ is the probability of finding the particle in the volume dτ.
With any Mains test series
Read the key points and the full model answer with a Mains test series
Every Mains test series (Civil Services, IFoS or Geo-Scientist) opens the solved IFoS Mains PYQ answers, the notes, the handbook and the daily answer archive until your Mains. The first test of each series is free. Civil Services and Geo-Scientist Mains PYQ solutions and Geo-Scientist Prelims PYQ solutions are free for everyone.
The full model answer
As written for the answer booklet: the diagram carries the working, the lines stay short. Read here only; it is not offered as a download.
CoversLaplaciande Broglie wavelengthpartial differential equationeigenvalue equationquantisation
All parts of Question 4
- 4(a)(i) Stark–Einstein law; why the quantum yield is often low10 marks
- 4(a)(ii) Surface area of silica gel from the nitrogen monolayer10 marks
- 4(b) Standard and actual potential of the Cu / Fe³⁺, Fe²⁺ cell10 marks
- 4(c) Schrödinger wave equation in three dimensions; meaning of ψ and ψ²10 marks