Question

As you know, in the Schrodinger representation, the wavefunction is time-dependent while the operator is time-independent....

As you know, in the Schrodinger representation, the wavefunction is time-dependent while the operator is time-independent. In the Heisenberg representation, the wavefunction is time-independent while the operator is generally time-dependent.

However, only the Hamiltonian is time-independent in both representations of Schrodinger and Heisenberg. Why?

Describe the reason for that clearly.

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Answer #1

Wavefunction is basically give the probability amplitude of particle finding at any position x and time t and is represented as , because probability can vary with time , also sometime operator can also vary with time to find the particle parameter like momentum at a particular time .

But only quantity which always remains constant with time is the total energy of particle which always remains fixed and cannot be vary with time and position and total energy is basically represented by the Hamiltonian.

This is the reason why Hamiltonian always remain independent of time.

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