Question

What is the Hamiltonian operator in chemistry?

Answer 1

Hamiltonian operator:

1. It is the summation of the kinetic and potential energy operator.
2. The operator of kinetic energy should be the same for all the models but potential energy changes as per the parameters.
3. It is denoted the $\hat{\mathrm{H}}$ as an operator.

The description of the Hamiltonian operator is shown below:

1. It is used to calculate the system energy in terms of the wave function of quantum mechanics.
2. The input of this operator is wavefunction and the output is energy in the form of eigenvalues.
3. The wavefunction is the smallest amount of energy in the form of vibrational energy, also known as zero-point energy.
4. It is expressed in terms of momenta and position coordinates.
5. The formula for the Hamiltonian operator is: $\hat{\mathrm{H}}=\left(\frac{{\mathrm{p}}^2}{2\mathrm{m}}\right)+\mathrm{V}\left(\mathrm{x}\right)$, where the first term denotes the kinetic energy and the second term denotes the potential energy. In this equation, p is momentum, m is mass, and V is potential.
6. The operator is calculated in a particular direction of time.