Describing Force using potentials

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    Force Potentials
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Discussion Overview

The discussion revolves around the relationship between force and potential energy, particularly in the context of classical mechanics and its implications for quantum mechanics. Participants explore the derivation of the expression F = -dV/dx and its significance in conservative systems.

Discussion Character

  • Conceptual clarification
  • Technical explanation
  • Debate/contested

Main Points Raised

  • One participant expresses confusion about the derivation of the equation F = -dV/dx from Newton's second law, indicating a lack of understanding of how potentials relate to forces.
  • Another participant explains that in a conservative system, the force is defined as the gradient of the potential, suggesting that F = dV/dx, but expresses uncertainty about the negative sign.
  • A third participant clarifies that force is indeed the negative gradient of potential, emphasizing that this is a classical physics concept rather than a quantum one.
  • A later reply acknowledges the negative sign's significance, stating it relates to the behavior of potential energy at infinity and its relevance to Schrödinger's equation in quantum mechanics.

Areas of Agreement / Disagreement

Participants generally agree on the relationship between force and potential in conservative systems, but there is some uncertainty regarding the interpretation of the negative sign in the equation. The discussion does not reach a consensus on the derivation specifics.

Contextual Notes

Participants reference classical mechanics and its application to quantum mechanics, highlighting the need for clarity in definitions and the implications of potential energy behavior at infinity. There are unresolved questions about the derivation and interpretation of the equations discussed.

randybryan
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Just started revision for Quantum Mechanics after a very long break so everything is a bit rusty. Don't have anyone nearby at hand to ask, so hoping someone here will help.

Been given Newton's second law of motion as

F= m d^2 x/ dt^2

which is a second order equation hence requiring two initial conditions, often given as x(t=0) and dx/dt (t=0). Then, to quote from my lecture notes, ''In quantum mechanics, we will work with potentials, rather than forces, so we will be restricted to conservative systems where energy is constant. The aboe Newton's law equation can be written as

AND THIS IS WHERE I CAN'T DEDUCE WHAT'S GOING ON

F= md^2x/dt^2 = -dV/dx

Where does the -dV/dx come from? I know this is a potential, but I don't know how it was derived
 
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hi randybryan! :smile:

(try using the X2 icon just above the Reply box :wink:)
randybryan said:
''In quantum mechanics, we will work with potentials, rather than forces, so we will be restricted to conservative systems where energy is constant. The aboe Newton's law equation can be written as

AND THIS IS WHERE I CAN'T DEDUCE WHAT'S GOING ON

F= md^2x/dt^2 = -dV/dx

Where does the -dV/dx come from? I know this is a potential, but I don't know how it was derived

"conservative system" means that the force F is conservative, ie that it is the gradient of a potential, V

in other words: by definition F.i = dV/dx (i'm not sure about the "minus" :confused:)
 
tiny-tim said:
hi randybryan! :smile:

(try using the X2 icon just above the Reply box :wink:)


"conservative system" means that the force F is conservative, ie that it is the gradient of a potential, V

in other words: by definition F.i = dV/dx (i'm not sure about the "minus" :confused:)


Force is the minus gradient of potential. And this is a classical physics question, not quantum.
 
Thanks guys, it all makes sense now!

The reason it is negative is because it tends to zero at infinity as it moves away from potential well.

The only reason I put it in Quantum physics section is because it is used to rationalise Schrodingers equation
 

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