Question

What is the Hamiltonian operator in chemistry?

Answer 1

Hint: We need to know that the concept of Hamiltonian operator comes under the class of quantum chemistry. This chemistry focuses on the application of quantum mechanics to chemical systems. Quantum chemistry studies the ground state of individual atoms and molecules, and the excited states, and transition states that occur during chemical reactions.

Complete answer:
Now let’s understand what is the Hamiltonian operator? The molecular Hamiltonian is the Hamiltonian operator representing the energy of the electrons and nuclei in a molecule. This operator and the associated Schrödinger equation play a vital role in computational chemistry and physics for computing properties of molecules and aggregates of molecules, such as thermal conductivity, specific heat, electrical conductivity, optical, and magnetic properties, and reactivity. In quantum mechanics, the Hamiltonian of a system is an operator corresponding to the total energy of that system, including both kinetic energy and potential energy. Due to its close relation to the energy spectrum and time-evolution of a system, it is of fundamental importance in most formulations of quantum theory.
\[H \wedge \psi = E\psi \]
Where\[H \wedge \]is the Hamiltonian operator, E is the energy of the particle and \[\psi \] is the particle's wave function that describes its spatial probability. The Hamiltonian operator is the sum of the kinetic energy operator and potential energy operator.

Note:
We need to know that the Hamiltonian itself does not technically have any units. As an operator, it is something that, when applied to a wave function, reveals the possible energies of the wave function. The kinetic energy operator is the same for all models but the potential energy changes and is the defining parameter.