# Theoretical Background

Chapter

## Abstract

Inadequate descriptions of atoms and molecules by the methods of classical physics led researchers to propose new ways to describe physical reality, giving birth to a totally new science, quantum mechanics. The methods of quantum mechanics are based on the introduction of a wave function, whose physical meaning is related to the probability of finding a certain particle, at a certain time in a volume element, positioned between
or for short,

*x*and*x*+*dx*in the*x*= direction, between*y*and*y*+*dy*in the*y*= direction, and between*z*and*z*+*dz*in the*z*= direction at certain time*t*. This wave function Ψ satisfies the Schrödinger equation,$$
\left( { - \frac{{{\hbar ^2}}}{{2m}}{\nabla ^2} + v} \right)\Psi = {\rm E}\Psi,\hbar = \frac{h}{{2\pi }}, $$

*H*Ψ =*E*Ψ, where*H*, the Hamiltonian operator, is defined by the expression$$
H = - \frac{{{\hbar ^2}}}{{2m}}{\nabla ^2} + V;
$$

*h*is Planck’s constant; ∇^{2}is the sum of the partial second derivatives with respect to*x*,*y*, and*z*;*m*is the mass of the particle; and*V*is the potential energy of the system. The Hamiltonian*H*represents the quantum equivalent of the sum of the kinetic energy and potential energy, with*V*being the potential energy operator and \( \frac{{ - {\hbar ^2}}}{{2m}}{\nabla ^2} \) the kinetic energy operator. Finally,*E*is the total energy of the system and is a number, not an operator.### Keywords

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### References

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*Cancer Investigation*. To be published.Google Scholar - 2.Sapse, A.M., Schweitzer, B.S., Dicker, A.P., Bertino, J.R., and Frecer, V.
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### Bibliography

- Foresman, J.B., and Frisch, A.
*Exploring Chemistry with Electronic Structure Methods*. Gaussian Inc., Pittsburgh, PA, 1993.Google Scholar - Hehre, W.J., Radom, L., Schleyer, P.V.R., and Pople, J.A.
*Ab Indio Molecular Theory*. John Wiley & Sons, New York, 1986.Google Scholar - Levine, I.N.
*Quantum Chemistry*. Prentice Hall, Englewood Cliffs, New Jersey, 1991.Google Scholar - Schaefer III, H.F.
*Applications of Electronic Structure Theory*. Plenum Press, New York and London, 1977.CrossRefGoogle Scholar

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