Calculate an approximate ground-state energy of the hydrogen atom using 1 function o(r) = re-ar, where a is the variational parameter. How does this approximate gy compare to the exact energy of the hydrogen atom?
Calculate an approximate ground-state energy of the hydrogen atom using 1 function o(r) = re-ar, where a is the variational parameter. How does this approximate gy compare to the exact energy of the hydrogen atom?
Chemistry
10th Edition
ISBN:9781305957404
Author:Steven S. Zumdahl, Susan A. Zumdahl, Donald J. DeCoste
Publisher:Steven S. Zumdahl, Susan A. Zumdahl, Donald J. DeCoste
Chapter1: Chemical Foundations
Section: Chapter Questions
Problem 1RQ: Define and explain the differences between the following terms. a. law and theory b. theory and...
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Transcribed Image Text:**Variational Method for Ground-State Energy of Hydrogen Atom**
**Objective:**
Calculate an approximate ground-state energy of the hydrogen atom using a trial function \( \phi(r) = r e^{-\alpha r} \), where \( \alpha \) is the variational parameter.
**Task:**
How does this approximate energy compare to the exact energy of the hydrogen atom?
In this exercise, the trial function for estimating the ground-state energy of the hydrogen atom is given as a function of the radial distance \( r \) from the nucleus. The parameter \( \alpha \) can be adjusted to minimize the energy and provide a better approximation.
Note: This method is part of the variational principle in quantum mechanics, which helps in estimating the lower bounds on the energy states.
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