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Problem 3. May the fourth be with you potential U(x) = kx4, where k > 0....
5. Consider a particle moving in the region x>0 under the influence of the potential U(x)...
5. Consider a particle moving in the region x>0 under the influence of the potential U(x) = C (a/x + x/a), where C=1J, and a=2m. (a) Find the equilibrium positions and determine whether they are stable or unstable. (b) Find U at those equilibrium positions. (c) Sketch U(x) without using a computer (explain how you get the sketch) and discuss the motion of the particle in details in all the different regions if its total energy E1 = 2 J,...
A particle is introduced to a region with a potential described by U(x)--2x2 +x*+1 Joules. 3. a. ...
A particle is introduced to a region with a potential described by U(x)--2x2 +x*+1 Joules. 3. a. (2 pts) In software, plot the potential U) Set your axis ranges: -2 SxS2 and 0s b. (5 pts) Find the equilibrium positions and determine whether they are stable or c. (8 pts) Describe the motion of the particle for total energy values E-О.0.05. 1.0, 2.0 unstable. Explain how you arrived at your answers. (all in Joules). What I am looking for here...
A particle of mass m moves in one dimension. Its potential energy is given by U(x)...
A particle of mass m moves in one dimension. Its potential energy is given by U(x) = -Voe-22/22 where U, and a are constants. (a) Draw an energy diagram showing the potential energy U(). Choose some value for the total mechanical energy E such that -U, < E < 0. Mark the kinetic energy, the potential energy and the total energy for the particle at some point of your choosing. (b) Find the force on the particle as a function...
A particle moves and has a potential energy that can be described by the equation U(x)...
A particle moves and has a potential energy that can be described by the equation U(x) = 4 sin(2 x) where U(x) is in J. The total energy of the particle is E_tot = 2 J. Make a well-labelled graph of U(x)vs. x from x = 0 to x = pi. Draw a line corresponding to E_tot on your diagram. Assume the particle is moving in the positive x direction. Where is the particle speeding up? Make sure you solve...
I can do the first problem which is show the motion is periodic. The rest questions...
I can do the first problem which is show the motion is
periodic. The rest questions are hard for me. I found a similar
question on the p27 of ‘mechanics’ by landau which shows on the
second picture
But I can’t understand the math. Please help.
Assigment 1.2. [10 points] A particle of mass m moves along x axis under the action of the force F--kx2n1 where n is an integer number. Show that this motion is periodic [2 points]....
A particle is confined to move in x-direction between x=0 and x= 0, and it experiences...
A particle is confined to move in x-direction between x=0 and x= 0, and it experiences an conservative force F(x) such that its potential energy U(x) = -bx².ex , where a, b>0, (a) Determine this conservative force F(x) as a function of x, (b) At the equilibrium point x = S, F(S) = 0, determine the value of S. (c) If the particle is moving around S, and if we define z =x-S, write down the equation of motion of...
A particle is moving to the right with initial kinetic energy To, subject to a force...
A particle is moving to the right with initial kinetic energy To, subject to a force F(z)k function U(x) for this force ; (b) the kinetic energy and (c) the total energy of the particle as a function of its position; (d) find the turning points of the motion and the condition the total energy of the particle must satisfy if its motion is to exhibit turning points. (e) Sketch the potential, kinetic and total energy function (you can use...
Consider a potential well defined as U(x) = for x < 0, U(x) = 0 for 0 < x < L, and U(x) = U0 > 0 for x > L (see the following figure).
Consider a potential well defined as \(U(x)=\infty\) for \(x<0, U(x)=0\)for \(0<x<L,\)and \(U(x)=U_{0}>0\) for \(x>L\) (see the following figure). Consider a particle with mass \(m\) and kinetic energy \(E<U_{0}\)that is trapped in the well. (a) The boundary condition at the infinite wall ( \(x=\)0) is \(\psi(x)=0\). What must the form of the function \(\psi(x)\) for \(0<x<L\)be in order to satisfy both the Schrödinger equation and this boundary condition? (b) The wave function must remain finite as \(x \rightarrow \infty\). What must...
The figure below shows a plot of potential energy U versus position x of a 1.04...
The figure below shows a plot of potential energy U
versus position x of a 1.04 kg particle that can travel
only along an x axis. (Nonconservative forces are not
involved.) In the graphs, the potential energies are
U1 = 15 J, U2 = 30 J, and
U3 = 40 J.
The figure below shows a plot of potential energy U versus position x of a 1.04 kg particle that can travel only along an x axis. (Nonconservative forces are...
(III) Quantum Tunneling Consider an electron in 1D in presence of a potential barrier of width...
(III) Quantum Tunneling Consider an electron in 1D in presence of a potential barrier of width L represented by a step function ſo I<0 or 1>L V U. r>0 and 2<L The total wavefunction is subject to the time-independent Schrödinger equation = EV (2) 2m ar2 +V where E is the energy of the quantum particle in question and m is the mass of the quantum particle. A The total wavefunction of a free particle that enters the barrier from...
5. Consider a particle moving in the region x>0 under the influence of the potential U(x) = C (a/x + x/a), where C=1J, and a=2m. (a) Find the equilibrium positions and determine whether they are stable or unstable. (b) Find U at those equilibrium positions. (c) Sketch U(x) without using a computer (explain how you get the sketch) and discuss the motion of the particle in details in all the different regions if its total energy E1 = 2 J,...
A particle is introduced to a region with a potential described by U(x)--2x2 +x*+1 Joules. 3. a. (2 pts) In software, plot the potential U) Set your axis ranges: -2 SxS2 and 0s b. (5 pts) Find the equilibrium positions and determine whether they are stable or c. (8 pts) Describe the motion of the particle for total energy values E-О.0.05. 1.0, 2.0 unstable. Explain how you arrived at your answers. (all in Joules). What I am looking for here...
A particle of mass m moves in one dimension. Its potential energy is given by U(x) = -Voe-22/22 where U, and a are constants. (a) Draw an energy diagram showing the potential energy U(). Choose some value for the total mechanical energy E such that -U, < E < 0. Mark the kinetic energy, the potential energy and the total energy for the particle at some point of your choosing. (b) Find the force on the particle as a function...
A particle moves and has a potential energy that can be described by the equation U(x) = 4 sin(2 x) where U(x) is in J. The total energy of the particle is E_tot = 2 J. Make a well-labelled graph of U(x)vs. x from x = 0 to x = pi. Draw a line corresponding to E_tot on your diagram. Assume the particle is moving in the positive x direction. Where is the particle speeding up? Make sure you solve...
I can do the first problem which is show the motion is
periodic. The rest questions are hard for me. I found a similar
question on the p27 of ‘mechanics’ by landau which shows on the
second picture
But I can’t understand the math. Please help.
Assigment 1.2. [10 points] A particle of mass m moves along x axis under the action of the force F--kx2n1 where n is an integer number. Show that this motion is periodic [2 points]....
A particle is confined to move in x-direction between x=0 and x= 0, and it experiences an conservative force F(x) such that its potential energy U(x) = -bx².ex , where a, b>0, (a) Determine this conservative force F(x) as a function of x, (b) At the equilibrium point x = S, F(S) = 0, determine the value of S. (c) If the particle is moving around S, and if we define z =x-S, write down the equation of motion of...
A particle is moving to the right with initial kinetic energy To, subject to a force F(z)k function U(x) for this force ; (b) the kinetic energy and (c) the total energy of the particle as a function of its position; (d) find the turning points of the motion and the condition the total energy of the particle must satisfy if its motion is to exhibit turning points. (e) Sketch the potential, kinetic and total energy function (you can use...
The figure below shows a plot of potential energy U
versus position x of a 1.04 kg particle that can travel
only along an x axis. (Nonconservative forces are not
involved.) In the graphs, the potential energies are
U1 = 15 J, U2 = 30 J, and
U3 = 40 J.
The figure below shows a plot of potential energy U versus position x of a 1.04 kg particle that can travel only along an x axis. (Nonconservative forces are...
(III) Quantum Tunneling Consider an electron in 1D in presence of a potential barrier of width L represented by a step function ſo I<0 or 1>L V U. r>0 and 2<L The total wavefunction is subject to the time-independent Schrödinger equation = EV (2) 2m ar2 +V where E is the energy of the quantum particle in question and m is the mass of the quantum particle. A The total wavefunction of a free particle that enters the barrier from...
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