What is the relationship between total energy and momentum for a free particle as described by the Schrödinger wave equation?
Understand the Problem
The question is discussing the Schrödinger wave equation and its application to a free particle, specifically how total energy relates to momentum and wave properties.
Answer
E = p^2/2m and ℏω = ℏ^2k^2/2m.
The relationship between total energy and momentum for a free particle is given by E = p^2/2m. In the de Broglie formulation, this becomes ℏω = ℏ^2k^2/2m, where ω is the angular frequency and k is the wave number.
Answer for screen readers
The relationship between total energy and momentum for a free particle is given by E = p^2/2m. In the de Broglie formulation, this becomes ℏω = ℏ^2k^2/2m, where ω is the angular frequency and k is the wave number.
More Information
The relationship describes a free particle in quantum mechanics with zero potential energy, represented by a wave function. The de Broglie relation connects wave-like and particle-like properties.
Tips
Ensure units are consistent when calculating energy and momentum.
Sources
- 5.1: The Free Particle - Chemistry LibreTexts - chem.libretexts.org
- The Schrödinger Equation in One Dimension - faculty.chas.uni.edu
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