Which of the following represents the kinetic energy calculation for a Slater determinant? A) T_s[ρ] = rac{1}{N} rac{d^2}{dr^2} ψ B) T_s[ρ] = - rac{1}{2} ra{ψ}|−∇^2|ψ ext{m} C)... Which of the following represents the kinetic energy calculation for a Slater determinant? A) T_s[ρ] = rac{1}{N} rac{d^2}{dr^2} ψ B) T_s[ρ] = - rac{1}{2} ra{ψ}|−∇^2|ψ ext{m} C) T_s[ρ] = ra{ψ}|−∇|ψ D) T_s[ρ] = rac{1}{2} rac{d^2}{dx^2} ρ
Understand the Problem
The question is asking which option correctly represents the kinetic energy calculation in the context of a Slater determinant. This involves understanding the mathematical formulations for kinetic energy in quantum mechanics related to the Slater determinant, which is a way to describe the wave function of multiple fermions. We need to evaluate the given options to determine which one is accurate.
Answer
B) T_s[ρ] = -\frac{1}{2} \bra{\text{ψ}}|- abla^2|\text{ψ}\rangle.
The final answer is B) T_s[ρ] = - rac{1}{2} ra{ ext{ψ}}|- abla^2| ext{ψ} angle.
Answer for screen readers
The final answer is B) T_s[ρ] = - rac{1}{2} ra{ ext{ψ}}|- abla^2| ext{ψ} angle.
More Information
The kinetic energy in quantum mechanics for Slater determinants involves integrating over a squared differential operator applied to a wavefunction. This captures how kinetic energy is calculated within the framework of quantum systems described by Slater determinants.
Tips
A common mistake is confusing different mathematical operators. Ensure to note the operators used in describing kinetic energy in quantum mechanics.
Sources
- Slater determinant - Wikipedia - en.wikipedia.org
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