A particle subject to a potential V (x) has the form 1/ cosh(kx). Obtain an expression for V (x) and the value of the corresponding energy level.
A particle subject to a potential V (x) has the form 1/ cosh(kx). Obtain an expression for V (x) and the value of the corresponding energy level.
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A particle subject to a potential V (x) has the form 1/ cosh(kx). Obtain an expression for V (x) and the value of the corresponding energy level.
E70.1(a) Construct the potential energy operator of a particle with potential energy V(x)={kx, where k is...
E70.1(a) Construct the potential energy operator of a particle with potential energy V(x)={kx, where k is a constant.
Suppose a particle has zero potential energy for x < 0, a constant value V, for...
Suppose a particle has zero potential energy for x < 0, a constant value V, for 0 ≤ x ≤ L, and then zero for x > L. Sketch the potential. Now suppose that wavefunction is a sine wave on the left of the barrier, declines exponentially inside the barrier, and then becomes a sine wave on the right, being continuous everywhere. Sketch the wavefunction on your sketch of the potential energy.
Suppose a particle has zero potential energy for x < 0, a constant value V, for...
Suppose a particle has zero potential energy for x < 0, a constant value V, for 0 ≤ x ≤ L, and then zero for x > L. Sketch the potential. Now suppose that wavefunction is a sine wave on the left of the barrier, declines exponentially inside the barrier, and then becomes a sine wave on the right, being continuous everywhere. Sketch the wavefunction on your sketch of the potential energy.
For a particle of mass m, consider a Morse potential of V. V(x) cosh (Bx)' where...
For a particle of mass m, consider a Morse potential of V. V(x) cosh (Bx)' where V> 0 and 8 >0. (a) Illustrate this potential graphically as a function of x. (b) Write the WKB quantization condition: of pladě = (n+ + ) 7, n=0,1,2,3,,.... in terms of the bound state energies En and V(x). What are I'min and Imax in this case, and what is the physical meaning/interpretation of Imin and Imax ? (C) Use WKB methods to determine...
. A particle is subject to the potential shown below: v (x) 5 V(x)-k2, when 0...
. A particle is subject to the potential shown below: v (x) 5 V(x)-k2, when 0 S.x S oo v(x)= oo, when-oo < x 0 2 0.5 1.5 The wave function for the ground state is Determine the normalization constant C for this wave function.
Consider a particle of mass m moving in a one-dimensional potential of the form V. for...
Consider a particle of mass m moving in a one-dimensional potential of the form V. for 0<x<b, V(a) = 0 for Islal<e, for 1212, with V., b and c positive constants and c>b. a Explain why the wave function of the particle can be assumed to be cither an even function or an odd function of a. b For the case that the energy E of the particle is in the range 0<ESV., find the (unnormalized) even cigenfunctions and give...
A particle of mass m is in a potential energy field described by, V(x, y) =...
A particle of mass m is in a potential energy field described by, V(x, y) = 18kx² +8ky? where k is a positive constant. Initially the particle is resting at the origin (0,0). At time t = 0 the particle receives a kick that imparts to it an initial velocity (vo, 2vo). (a) Find the position of the particle as a function of time, x(t) and y(t). (b) Plot the trajectory for this motion (Lissajous figure) using Vo = 1,...
3. A particle subject only to conservative forces has the potential energy vs. position curve shown...
3. A particle subject only to conservative forces has the potential energy vs. position curve shown to the right. The function for the potential is: U(x)-k where γ 1.00 J.m2 and k-7.00 Jr. The particle has a mass of 3.00 kg. (a) Calculate the force on the particle as a function of position, F(x). (b) At which points, (A, B, C, D), must the particle be placed at rest such that it will stay at rest? Why must the particle...
A particle of mass 5 kg is subject to a conservative force whose potential energy (in...
A particle of mass 5 kg is subject to a conservative force whose potential energy (in joules) as a function of position (in meters) is given by the equation U(x) =-100x5e-1x [where x > 0] (a) Determine the position xo where the particle experiences stable equilibrium (b) Find the potential energy Uo of the particle at the position x 2106 The particle is displaced slightly from position x = xo and released (c) Determine the effective value of the spring...
1. A particle is described by wave function: = A exp(-alphax^2). Find the potential energy V(x)...
1. A particle is described by wave function: = A exp(-alphax^2). Find the potential energy V(x) with V(0)=0. And what is the energy of the particle?
E70.1(a) Construct the potential energy operator of a particle with potential energy V(x)={kx, where k is a constant.
For a particle of mass m, consider a Morse potential of V. V(x) cosh (Bx)' where V> 0 and 8 >0. (a) Illustrate this potential graphically as a function of x. (b) Write the WKB quantization condition: of pladě = (n+ + ) 7, n=0,1,2,3,,.... in terms of the bound state energies En and V(x). What are I'min and Imax in this case, and what is the physical meaning/interpretation of Imin and Imax ? (C) Use WKB methods to determine...
. A particle is subject to the potential shown below: v (x) 5 V(x)-k2, when 0 S.x S oo v(x)= oo, when-oo < x 0 2 0.5 1.5 The wave function for the ground state is Determine the normalization constant C for this wave function.
Consider a particle of mass m moving in a one-dimensional potential of the form V. for 0<x<b, V(a) = 0 for Islal<e, for 1212, with V., b and c positive constants and c>b. a Explain why the wave function of the particle can be assumed to be cither an even function or an odd function of a. b For the case that the energy E of the particle is in the range 0<ESV., find the (unnormalized) even cigenfunctions and give...
A particle of mass m is in a potential energy field described by, V(x, y) = 18kx² +8ky? where k is a positive constant. Initially the particle is resting at the origin (0,0). At time t = 0 the particle receives a kick that imparts to it an initial velocity (vo, 2vo). (a) Find the position of the particle as a function of time, x(t) and y(t). (b) Plot the trajectory for this motion (Lissajous figure) using Vo = 1,...
3. A particle subject only to conservative forces has the potential energy vs. position curve shown to the right. The function for the potential is: U(x)-k where γ 1.00 J.m2 and k-7.00 Jr. The particle has a mass of 3.00 kg. (a) Calculate the force on the particle as a function of position, F(x). (b) At which points, (A, B, C, D), must the particle be placed at rest such that it will stay at rest? Why must the particle...
A particle of mass 5 kg is subject to a conservative force whose potential energy (in joules) as a function of position (in meters) is given by the equation U(x) =-100x5e-1x [where x > 0] (a) Determine the position xo where the particle experiences stable equilibrium (b) Find the potential energy Uo of the particle at the position x 2106 The particle is displaced slightly from position x = xo and released (c) Determine the effective value of the spring...
1. A particle is described by wave function: = A exp(-alphax^2). Find the potential energy V(x) with V(0)=0. And what is the energy of the particle?
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