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.
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\\...
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...
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.
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...
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...
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...
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...
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...
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...
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...
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...
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...
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...
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...
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...
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...
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...
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...