What is the Schrödinger Wave Equation for a free particle and how is it related to the de Broglie formulation?
Understand the Problem
The question seems to be related to quantum mechanics, specifically discussing the Schrödinger Wave Equation and its applications to free particles. The focus is on energy expressions and the representation of free particles as infinite plane waves.
Answer
iħ∂Ψ/∂t = -ħ²/2m ∂²Ψ/∂x² for a free particle. Related to de Broglie's E = ħω, p = ħk.
The Schrödinger wave equation for a free particle is iħ∂Ψ/∂t = -ħ²/2m ∂²Ψ/∂x². It is related to the de Broglie formulation by expressing the particle's energy and momentum using wave properties: E = ħω and p = ħk, leading to E = p²/2m.
Answer for screen readers
The Schrödinger wave equation for a free particle is iħ∂Ψ/∂t = -ħ²/2m ∂²Ψ/∂x². It is related to the de Broglie formulation by expressing the particle's energy and momentum using wave properties: E = ħω and p = ħk, leading to E = p²/2m.
More Information
The free particle Schrödinger equation demonstrates wave-particle duality by representing quantum states as wave functions, combining elements of classical mechanics and wave theory.
Tips
Ensure energy and momentum are expressed as wave quantities using ħ for consistency with the de Broglie hypothesis.
Sources
- 3.1: The Schrödinger Equation - Chemistry LibreTexts - chem.libretexts.org
- Schrödinger equation - Wikipedia - en.wikipedia.org
- Understanding the de Broglie Wave Function - Physics Forums - physicsforums.com
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