The discussion centers around the conservation of energy in quantum systems, particularly in the context of time-dependent Hamiltonians. Participants explore the implications of time-varying potentials on energy conservation, examining both theoretical and conceptual aspects.
Participants express differing views on the implications of time-dependent Hamiltonians for energy conservation, with no consensus reached on whether energy can be conserved in such scenarios.
Participants reference various assumptions about invariance and the nature of Hamiltonians, but these assumptions are not universally agreed upon. The discussion includes unresolved mathematical considerations related to the time evolution of quantum states.
Then, where the energies gone? Whether the Hamiltonian is time-dependent, Schrödinger equation gives constant energy.gonadas91 said:Hi guys! one quick question, if in a quantum system the hamiltonian of a particle evolves with time (let's say, the potential is a function of t), the energy is not conserved right? I just want to be sure about this, thanks!
Then, the wave function have to vary depending on time to keep the energy as constant.gonadas91 said:But if you think of the hamiltonian as a matrix, that means that the matrix has different matrix elements for every different time, therefore its eigenvalues are not the same as time evolves.