There must be an example, and it could be found in the Classical mechanics by David Morin. In order for the Hamiltonian to be equal to the total energy, certain conditions must apply such as there must be no time dependence of the system. READ BOOK. That is the best. Go to library or download ebooks to acquire
In quantum mechanics, the commutator of the operator x with the Hamiltonian is equal to the momentum operator p.
Potential energy is equal to kinetic energy in a system when all of the potential energy has been converted into kinetic energy, typically at the point of maximum kinetic energy in the system.
You are referring to the Schrodinger Equation. This is because it comes from the classical view that the total energy is equal to the hamiltonian of a system:Kinetic Energy + Potential Energy = Total energy.Classically the kinetic energy is (1/2)mv2 = p2/(2m) ; where m is mass, v is velocity, p is momentum (p=mv).Now the momentum operator in QM is p=iħ∇ ;where ∇ is the gradient operator.This therefore yields the QM hamiltonian [-ħ2∇2/(2m) + V(x,y,z)]Ψ = EΨNow a more fun question to ask would be "Why is the Hamiltonian a function of the second-order partial differential with respect to position but the time dependent is only a function of a first-order differential with respect to time?"meaningHΨ = -iħ(dΨ/dt) or[-ħ2∇2/(2m) + V(x,y,z)]Ψ = -iħ(dΨ/dt)hint: Think Maxwell's Equations!
Mechanical energy is equal to potential energy plus kinetic energy in a closed system. The total mechanical energy is conserved.
Mechanical energy is equal to potential energy plus kinetic energy in a closed system. The total mechanical energy is conserved.
Mechanical energy is equal to potential energy plus kinetic energy in a closed system. The total mechanical energy is conserved.
Mechanical energy is equal to potential energy plus kinetic energy in a closed system. The total mechanical energy is conserved.
Mechanical energy is equal to potential energy plus kinetic energy in a closed system. The total mechanical energy is conserved.
Kinetic energy is equal to potential energy in a system when the object is at its highest point, such as at the top of a swing or at the peak of a roller coaster.
No, kinetic energy and potential energy are not equal in a system. Kinetic energy is the energy of motion, while potential energy is the energy stored in an object due to its position or state.
Mechanical energy is equal to potential energy plus kinetic energy in a closed system. The total mechanical energy is conserved.
In a system, potential energy and kinetic energy are not always equal. Potential energy is the energy stored in an object due to its position or state, while kinetic energy is the energy of motion. The total energy in a system is the sum of its potential and kinetic energy.