Question

The Schrödinger equation is fundamental to quantum mechanics because it describes

• A. The trajectory of a particle in a field
• B. The probability distribution of a particle's position and momentum
• C. The behavior of a classical wave
• D. The energy levels in a crystal lattice

Hint:

In quantum mechanics, think of the Schrödinger equation as the engine that predicts how the probability wave of a particle evolves in space and time.

Answer 1

The Correct Option is B

The Schrödinger equation is a key result in quantum mechanics. It governs the behavior of quantum systems by providing a wave function \( \psi \), which encodes the probability distribution of a particle’s position and momentum.
The time-independent Schrödinger equation is: \[ \hat{H} \psi = E \psi \] where \( \hat{H} \) is the Hamiltonian operator (representing total energy), \( \psi \) is the wave function, and \( E \) is the energy eigenvalue.
The square of the wave function's magnitude, \( |\psi(x)|^2 \), gives the probability density of finding the particle at a position \( x \). Therefore, the Schrödinger equation describes not a definite trajectory (as in classical mechanics), but a probability distribution of the particle’s observable quantities.
Why the other options are incorrect:

• (A) Trajectories are a classical concept; quantum mechanics replaces definite paths with probability distributions.
• (C) Classical waves follow the classical wave equation, not the Schrödinger equation.
• (D) Energy levels in a crystal lattice result from periodic potentials solved using the Schrödinger equation, but this is a specific case, not the general function.