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dEdt
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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. Why isn't this true in quantum mechanics?
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.