Describing Force using potentials

In summary, the conversation is about revising for Quantum Mechanics and the equation F= m d^2 x/ dt^2, which requires two initial conditions. The conversation also discusses the use of potentials rather than forces in quantum mechanics and the relationship between force and potential. It is concluded that the reason for the negative sign in the equation is because it tends to zero at infinity. The conversation was posted in the Quantum Physics section because the equation is used to rationalize Schrodingers equation.
  • #1
randybryan
52
0
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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  • #2
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:)
 
  • #3
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.
 
  • #4
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
 

1. What is a potential in relation to describing force?

A potential is a mathematical function that describes the relationship between the position and energy of a particle in a force field. It is used to calculate the force acting on the particle at any given point in the field.

2. How is a potential related to the concept of work?

A potential function is directly related to the concept of work. The work done by a force on a particle is equal to the change in potential energy of the particle. This means that the potential energy can be thought of as the stored work done on the particle by the force.

3. What is the difference between conservative and non-conservative forces in terms of potentials?

A conservative force can be described by a potential function, meaning that the work done by the force is path independent. Non-conservative forces, on the other hand, do not have a potential function and the work done by the force depends on the path taken by the particle.

4. How do potentials help in understanding the behavior of particles in a force field?

Potentials provide a way to mathematically describe the behavior of particles in a force field. By calculating the potential at different points in the field, we can determine the direction and magnitude of the force acting on the particle at those points.

5. Can potentials be used to describe all types of forces?

No, not all forces can be described using potentials. Only conservative forces, such as gravitational and electrostatic forces, can be described by a potential function. Non-conservative forces, like friction and air resistance, cannot be described using potentials.

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