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How is 'force' defined in quantum mechanics?

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In nonrelativistic quantum mechanics forces are added into the Hamiltonian of the system in terms of potenials. [math]F=ma[/math] can be written in the form [math]-\frac{dU(x)}{dx}=ma[/math]. read more

In nonrelativistic quantum mechanics forces are added into the Hamiltonian of the system in terms of potenials. [math]F=ma[/math] can be written in the form [math]-\frac{dU(x)}{dx}=ma[/math]. In this second form the force is expressed as a potential energy function of space. read more

In QM instead of force there is an operator of force in the momentum operator equation: $$\frac{d\hat{\vec{p}}}{dt}=\hat{\vec{F}}.$$ Operator (ordinary) equations for canonical variables are coupled and are difficult to solve for time-dependent non commuting variables. read more

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