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csutton1
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Does anyone have a momentum operator proof? The book I'm using is skipping a lot of steps .
csutton1 said:sorry i re-read my post and realized it was really vague. The momentum operator used to determine the momentum of a particle described by schrodingers wave equation.
malawi_glenn said:No JK423, that is not what you do. You want to show that the p operator is the generator of translations and that it fulfills certain commutation relations.
The momentum operator, denoted as p, is a mathematical operator used in quantum mechanics to describe the momentum of a particle. It is defined as the derivative of the position operator with respect to time.
The momentum operator is derived using the principles of quantum mechanics, specifically the wave-particle duality. It is obtained by applying the de Broglie relation (p = h/λ) to the Schrödinger equation, which describes the behavior of quantum particles.
The momentum operator is used to determine the momentum of a particle in a given quantum state. It is a fundamental quantity in quantum mechanics as it is related to the uncertainty principle, which states that the more precisely the momentum of a particle is known, the less precisely its position can be known.
The momentum operator is represented mathematically as a differential operator. In one-dimensional space, it is written as p = -iħ(d/dx), where i is the imaginary unit and ħ is the reduced Planck's constant. In three-dimensional space, it is written as p = (-iħ∇), where ∇ is the nabla operator.
The momentum operator is used in quantum mechanics to calculate the expectation value of the momentum of a particle in a given state. It is also used to determine the time evolution of a quantum system and to solve problems involving momentum in quantum mechanics.