Question

The Schrödinger equation is:

• A. \(H\psi = E\psi\)
• B. \(F = ma\)
• C. \(E = mc^2\)
• D. \(pV = nRT\)

Hint:

The equation \( H\psi = E\psi \) is a standard eigenvalue equation. Operating on the wavefunction with the total energy operator \( H \) returns the exact energy value \( E \) multiplied by the same wavefunction.

Answer 1

The Correct Option is A

Concept: The Schrödinger equation is the fundamental governing equation of non-relativistic quantum mechanics. Developed by Erwin Schrödinger in 1925, it describes how the quantum wave function of a physical system changes over time, playing a role analogous to Newton's laws of motion in classical mechanics.

Step 1: Analyze the time-independent formulation.
The stationary, time-independent Schrödinger equation can be expressed compactly using operator notation as an eigenvalue equation: \[ H\psi = E\psi \] Where:
• \( H \) is the Hamiltonian operator, which represents the total energy operator of the system (the sum of kinetic and potential energies).
• \( \psi \) (psi) is the wavefunction of the system, containing all accessible physical information about the state.
• \( E \) is a scalar constant representing the total energy eigenvalue of that specific quantum state.

Step 2: Verify the options.
Let's check the alternative equations:
• \( F = ma \): Newton's Second Law of Motion (Classical Mechanics).
• \( E = mc^2 \): Einstein's Mass-Energy Equivalence relation (Special Relativity).
• \( pV = nRT \): The Ideal Gas Law (Thermodynamics). Thus, Option (A) is the correct mathematical statement of the Schrödinger equation.