Which of the following functions can be normalized (in all cases the range for x is from x = −∞ to ∞, and a is a positive constant): (i) sin(ax);(ii) cos(ax) e-x^2? Which of these functions are acceptable as wavefunctions?

Which of the following functions can be normalized (in all cases the range for x is from x = −∞ to ∞, and a is a positive constant): (i) sin(ax);(ii) cos(ax) e-x^2? Which of these functions are acceptable as wavefunctions?

Physical Chemistry

2nd Edition

ISBN:9781133958437

Author:Ball, David W. (david Warren), BAER, Tomas

Publisher:Ball, David W. (david Warren), BAER, Tomas

Chapter11: Quantum Mechanics: Model Systems And The Hydrogen Atom

Section: Chapter Questions

Problem 11.61E: What is the physical explanation of the difference between a particle having the 3-D rotational...

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Quantum chemistry deals with the properties of chemical systems and their reactions. The branch of chemistry which is more concerned with quantum chemistry is physical chemistry. It is a more sophisticated field of theoretical physics which is concerned towards the application of physical concepts towards various chemical aspects such as, formation of atoms, chemical structure descriptions, chemical bond strength, hybridization, conjugation etc. Quantum chemistry mainly studies the various states i.e., ground state, excited state, transition states of the individual atoms or molecules taking place during any chemical reaction. The laws of motion explained by various scientists, which are termed as “classical mechanics” were not acceptable in terms of electrons, protons, atoms, light etc. Thus, a new theory named “quantum mechanics” emerged to understand the basic framework of various atomic and subatomic particles.

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Which of the following functions can be normalized (in all cases the range for x is from x = −∞ to ∞, and a is a positive constant): (i) sin(ax);
(ii) cos(ax) e^{-x^2}? Which of these functions are acceptable as wavefunctions?

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Which of the following functions can be normalized (in all cases the range for x is from x = −∞ to ∞, and a is a positive constant): (i) e-ax^2; (ii) e–ax. Which of these functions are acceptable as wavefunctions?
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