Replacing the energy by the energy operator and the momentum by the momentum operator in the four-momentum, one obtains the four-momentum operator, used in relativistic wave equations.
22.
It is possible to write the quantum mechanical kinetic energy operator for such curvilinear coordinates, but it is hard to formulate a general theory applicable to any molecule.
23.
At the quantum level, translations in would be generated by a " Hamiltonian ", where " E " is the energy operator and is the " ordinary " Hamiltonian.
24.
As written, the first two terms are the kinetic energy operators of the two electrons, the third term is the harmonic electron-nucleus potential, and the final term the electron-electron interaction potential.
25.
"Think how big this merger would have been under the numbers of 20 years ago, " said David Garlick of the Texas Independent Royalty Owners Association, the trade group of Texas'independent energy operators.
26.
They observed that many vertex algebras that appear in nature have a useful additional structure ( an action of the Virasoro algebra ), and satisfy a bounded-below property with respect to an energy operator.
27.
The kinetic-energy operator in the Hamiltonian scales as 1 / r _ s ^ 2, where r _ s is the Wigner-Seitz radius, whereas the interaction energy operator scales as 1 / r _ s.
28.
The kinetic-energy operator in the Hamiltonian scales as 1 / r _ s ^ 2, where r _ s is the Wigner-Seitz radius, whereas the interaction energy operator scales as 1 / r _ s.
29.
There is a 4 ?4 identity matrix pre-multiplying the energy operator ( including the potential energy term ), conventionally not written for simplicity and clarity ( i . e . treated like the number 1 ).
30.
Applying these ladder operators to the eigenstates | " ! " 0 of the total angular momentum, azimuthal angular momentum and energy operators, the eigenvalues of the first Casimir operator, 1, are seen to be quantized,.
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