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Is the potential operator (in positional/space basis) of the Hamiltonian always diagonal in that basis? And is the kinetic energy operator always diagonal in complementary momentum space?
A potential operator in positional space is a mathematical operator that represents the potential energy of a particle in a given position. It is typically denoted as V(x), where x is the position of the particle.
The potential operator, along with the kinetic energy operator, is a component of the Hamiltonian operator, which represents the total energy of a system. The potential operator is responsible for accounting for the potential energy of a particle in a given position.
In quantum mechanics, the potential operator is used to calculate the energy states of a particle in a given position. It is an essential component in solving the Schrödinger equation and predicting the behavior of quantum systems.
Yes, the potential operator can be applied to systems with multiple particles. In this case, the operator becomes a function of the positions of all the particles and is denoted as V(x1, x2, ..., xn).
The potential operator is a mathematical operator that acts on a wave function to determine the potential energy of a particle in a given position. The potential function, on the other hand, is a mathematical function that describes the potential energy of a system as a function of position. While the potential operator is used in quantum mechanics, the potential function is more commonly used in classical mechanics.