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- TL;DR Summary
- Wondering about the origins of the Momentum and Energy Operators, i want to know how they are derived, assuming we have no knowlegde of the Schrødinger Equation.
So we all know that the form of the momentum operator is: iħd/dx. And for energy it is iħd/dt. But how do we derive these operators?
The only derivations of the i have seen is where the schrødinger equation was used, but that makes the logic circular, because the Schrødinger-Equation is derived from the momentum operator applied to the classical hamiltonian?
So i am interested in knowing other ways to derive the momentum and energy operators, from first principles. Can anyone help?I have read about cannonical quantization, where you postulate that [p,x]=iħ, and this should appereantly give the form of p=ih*d/dx, if we insist that x is diagonal. Has anyone heard of this?
Any contribution is deeply appreciated!
The only derivations of the i have seen is where the schrødinger equation was used, but that makes the logic circular, because the Schrødinger-Equation is derived from the momentum operator applied to the classical hamiltonian?
So i am interested in knowing other ways to derive the momentum and energy operators, from first principles. Can anyone help?I have read about cannonical quantization, where you postulate that [p,x]=iħ, and this should appereantly give the form of p=ih*d/dx, if we insist that x is diagonal. Has anyone heard of this?
Any contribution is deeply appreciated!