What is Newton equations: Definition and 19 Discussions

The Schrödinger–Newton equation, sometimes referred to as the Newton–Schrödinger or Schrödinger–Poisson equation, is a nonlinear modification of the Schrödinger equation with a Newtonian gravitational potential, where the gravitational potential emerges from the treatment of the wave function as a mass density, including a term that represents interaction of a particle with its own gravitational field. The inclusion of a self-interaction term represents a fundamental alteration of quantum mechanics. It can be written either as a single integro-differential equation or as a coupled system of a Schrödinger and a Poisson equation. In the latter case it is also referred to in the plural form.
The Schrödinger–Newton equation was first considered by Ruffini and Bonazzola in connection with self-gravitating boson stars. In this context of classical general relativity it appears as the non-relativistic limit of either the Klein–Gordon equation or the Dirac equation in a curved space-time together with the Einstein field equations.
The equation also describes fuzzy dark matter, and approximates classical cold dark matter described by the Vlasov–Poisson equation in the limit that the particle mass is large.Later on it was proposed as a model to explain the quantum wave function collapse by Lajos Diósi and Roger Penrose, from whom the name "Schrödinger–Newton equation" originates. In this context, matter has quantum properties while gravity remains classical even at the fundamental level. The Schrödinger–Newton equation was therefore also suggested as a way to test the necessity of quantum gravity.In a third context, the Schrödinger–Newton equation appears as a Hartree approximation for the mutual gravitational interaction in a system of a large number of particles. In this context, a corresponding equation for the electromagnetic Coulomb interaction was suggested by Philippe Choquard at the 1976 Symposium on Coulomb Systems in Lausanne to describe one-component plasmas. Elliott H. Lieb provided the proof for the existence and uniqueness of a stationary ground state and referred to the equation as the Choquard equation.

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  1. Sam Jelly

    Proving the gravitational force of a solid sphere using integration

    This is my attempt at the solution. x from the equation dF = GmdM/x^2 represents the distance between the circular plate’s center of mass and mass m.
  2. Venturi365

    Find the unkown tensions and masses in the situation below

    TL;DR Summary: I don't know if my procedure is correct in this excercise I've tried to solve this problem but I find my solution unintuitive and I think I might be wrong. First of all, applying Newton's Laws I calculated the value for ##T_1## like this: $$ \begin{align} \sum F_{x} &=0\\...
  3. hjam24

    Determine vertical velocity vector on sloped surface

    A golf is launched at a speed v,f and launch angle, β,f. The slope of the green is equal to φ. At some point the ball is located on the rim of a hole. The side view (a) and overhead view (b) looks as in the attached image.According to the author of the [paper][2] "The Physics of Putting" the...
  4. A

    I Why Is Moving Backwards on Skates Challenging for Humans?

    Can we apply Newton's laws of motion to the following use case mentioned below? Why is it difficult for Humans to move backwards with Skates? With practice & balance, is it possible to achieve this feat? Humans do can move backwards with their legs.
  5. Curtiss Oakley

    Problem involving energy/motion

    Homework Statement A ball of mass m=0.300 kg is connected by a strong massless rod of length L = 0.800 m to a pivot and held in place with the rod vertical. A wind exerts constant force F to the right on the ball as shown below. The ball is released from rest. The wind makes it swing up to...
  6. santimirandarp

    Relevant equations for an airplane landing

    The problem I'm pasting the problem below mainly for the plot of y vs x. A possible way to think of it I suppose the important thing here is to find y(t) with the condition that -amax<ay<amax, and vy(L/vp)=0 My attempt I've modeled acceleration as a(t)=-kt and got an equation for y(t) as...
  7. R

    I Sled Physics -- trouble understanding this equation

    In the classic example of a man on a sled being pushed down a hill, the equation involves the forces of gravity and friction: F = weight - friction or F = ma = mgsinθ-μkmgcosθ I do not understand why the push force at the start is not included in the equation. I assume that push force would...
  8. scott ketter

    What is the final velocity of a ball rolling through a tube?

    I am making a physics simulator and this problem is tricky. You have two freely moving objects with known masses and velocities in a frictionless environment. The first object is a ball and the second is a pipe. They are moving toward each other. I need to know what formulas are used to simulate...
  9. V

    Point of Maximal Tension for Vertical Circular Motion

    Homework Statement A heavy mass m is attached to thin wire and whirled in a vertical circle. Then the wire is most likely to break A only when mass is at the lowest B somewhere between lowest point and horizontal point C only when mass is horizontal D only when mass is at highest point...
  10. M

    Change in gravitational potential below the surface of the Earth

    Homework Statement Hi, Infinitely far away from a mass-->gravitational potential is zero. As get closer-->becomes negative. At surface-->it is the smallest value of r, i.e. the radius of the mass, hence the most negative value for gravitational potential. But as you go below surface of Earth...
  11. O

    Elastic Pendulum with Newton's equations of motion

    Homework Statement A pendulum with a mass m hanging on a elastic bug rigid massless rod which may swing in the xy-plane. The pivot point is the origin of the coordinate system. The force acting on the pendulum is the sum of force of an elastic central force directed towards the origin, and...
  12. V

    Please help me with this problem in static friction

    Homework Statement 2 Blocks connected by a string is placed on a rough horizontal floor,the coefficient of friction for block 1 is 0.2 while for block 2,it is 0.1. A force of 8N is applied on block 1 and a force of 1N is applied on block 2.Find the tension in the string and the frictional...
  13. knc

    Keep mass vertically still using friction

    A mass m1 is on a frictionless surface. To its right is a second mass m2 not touching the ground, but in the air. An applied force is applied towards the right of both masses. What is the minimum force needed so that the second object JUST starts to slip downwards...
  14. S

    What is the coefficient of friction in a child pulling a sled up an incline?

    Homework Statement A child pulls a 10lb sled up a 15 degree incline at a constant speed. The child is pulling on a rope attached to the sled. If the rope is inclined at 37 degrees to the horizontal and there is an 8 pound tension in the rope, what is the coefficient of friction?Homework...
  15. J

    Solving for different masses in pulley system with KE

    Homework Statement So I am stuck on this homework problem. I understand the general direction I have to take, but my algebra and physics aren't good. Here's the problem: A simple Atwood's machine uses two masses, m1 and m2. Starting from rest, the speed of the two masses is 10.0 m/s at the end...
  16. Quadrat

    Circular motion, tension and angular speed

    Homework Statement A ball with the mass m is attached to a rod, suspended by two strings both with lengths L. The rod is rotating with the angular velocity ω and the ball rotates with it in such a way that the strings are taut and the ball moves in a circular pattern. I tried to draw it on my...
  17. U

    Help to understand Newtons Law

    Homework Statement I am trying to understand a diagram I have of a gymnast hanging from a bar. She weighs 50kg and is not swinging, just hanging. In the diagram it has her weight as 500N (using 10/m/s/s for gravity * 50kg) but the bar she is hanging from has an upward arrow with 550 N next to...
  18. P

    Tension problem, finding acceleration with kinetic friction

    Three blocks are connected as shown in the uploaded picture. The strings and friction-less pulleys have negligible masses, and the coefficient of kinetic friction between the 2.0 kg block and the table is 0.17. What is the acceleration of the 2.0 kg block? Homework Equations ∑F = ma The...
  19. A

    I can not calculate these Newton equations

    A block B of 20 kg is trapped by a wire of 2 m a car A of 30 kg. Determine (a) the acceleration of the car (b) the tension of the wire, immediately after the system was abandoned the rest, in the position shown in the figure. Despise is the friction. Answer: (a) 6,17 m/s^2 (b) 144 N My...