Can you show an example of this?In classical mechanics, if there's an explicit time dependence in the Hamiltonian of a system, then it won't be equal to the system's total energy.
mfb said:Can you show an example of this?
A time-dependent Hamiltonian is a mathematical function that describes the dynamics of a system over time. It is used in quantum mechanics to calculate the evolution of a quantum system over time.
A time-independent Hamiltonian is a function that does not change with time, while a time-dependent Hamiltonian changes with time. Time-dependent Hamiltonians are often used to describe systems that are subject to external forces or are evolving over time.
The time-dependent Hamiltonian is a fundamental concept in quantum mechanics. It is used to calculate the time evolution of a quantum system and to predict the probabilities of different outcomes of observations or measurements.
The Schrödinger equation is a mathematical equation that describes the time evolution of a quantum system. The time-dependent Hamiltonian is a key component of the Schrödinger equation, as it determines the energy of the system and how it changes over time.
In most cases, time-dependent Hamiltonians cannot be solved analytically. However, there are some special cases where analytical solutions are possible, such as in simple harmonic oscillators or in certain time-dependent perturbation problems. In general, numerical methods are used to solve time-dependent Hamiltonians.