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annms
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What is the difference between the Hamiltonian operator and the Total energy operator? If both is used when working with total energy, why are there two different operators?
annms said:What is the difference between the Hamiltonian operator and the Total energy operator? If both is used when working with total energy, why are there two different operators?
The Hamiltonian operator is a mathematical representation of the total energy of a system in quantum mechanics, while the Total energy operator is a physical observable that represents the total energy of a system in classical mechanics.
The Hamiltonian operator is derived from the Total energy operator and includes all the terms necessary to fully describe the system's energy, such as kinetic energy and potential energy.
No, they cannot be used interchangeably. While they both represent the total energy of a system, they are used in different contexts and have different mathematical formulations.
The Hamiltonian operator is more commonly used in quantum mechanics as it is a fundamental concept in this field and is used to describe the dynamics of a system.
Yes, both the Hamiltonian operator and Total energy operator are linear operators and are represented by matrices in matrix mechanics. They also both have corresponding eigenvalues and eigenstates.