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Solved the probability of reflection R for a particle of mass m= 1.67 x 10-27kg and...
2.5 ty which will be discussed in chapter 4 2.3 Consider a particle of mass m...
2.5
ty which will be discussed in chapter 4 2.3 Consider a particle of mass m subject to a one-dimensional potential V(x) that is given by V = 0, x <0; V = 0, 0<x<a; V = Vo, x> Show that bound (E < Vo) states of this system exist only if k cotka = -K where k2 = 2mE/12 and k' = 2m(Vo - E)/h4. 2.4 Show that if Vo = 974/2ma, only one bound state of the system...
6. (20pts) Consider a particle of mass m and energy E approaching the step potential V(x)...
6. (20pts) Consider a particle of mass m and energy E approaching the step potential V(x) = { 0x< V.>0 x > 0 from negative values of x. Consider the case E> Vo. a) Classically, what is the probability of reflection? b) Quantum mechanically, what is the probability of reflection? Express your result in terms of the ratio VIE. What is the probability of reflection if E= 2Vo?
1. A particle of mass m moves in three dimensions, and has position r(t)-(x(t), y(t), z(t)) at ti...
Mechanics. Need help with c) and d)
1. A particle of mass m moves in three dimensions, and has position r(t)-(x(t), y(t), z(t)) at time t. The particle has potential energy V(x, y, 2) so that its Lagrangian is given by where i d/dt, dy/dt, dz/dt (a) Writing q(q2.93)-(r, y, z) and denoting by p (p,P2, ps) their associated canonical momenta, show that the Hamiltonian is given by (show it from first principles rather than using the energy) H(q,p)H(g1, 92,9q3,...
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,...
A particle slides along a straight wire so that a--k/v where a is the acceleration, v is the velocity and k-20 m3/s. The particle stars at X 0, t-0, with a speed vo 10 m/s. 2. When the particle is at...
A particle slides along a straight wire so that a--k/v where a is the acceleration, v is the velocity and k-20 m3/s. The particle stars at X 0, t-0, with a speed vo 10 m/s. 2. When the particle is at x = 4 m, the speed v is most nearly A. 2.49 m/s B. 3.46 m/s C. 5.29 m/s D. 6.93 m/s E. 7.50 m/s F. 8.62 m/s G. 8.88 m/s H. 9.13 m/s I 9.81 m/s J. 10.00...
A proton is projected in the positive x direction into aregion of uniform electric field E = -6.60 105i N/C att = 0....
A proton is projected in the positive x direction into
aregion of uniform electric field E = -6.60
105i N/C att = 0. The proton
travels 7.40 cm as it comes to rest.(a)
Formula for calculating the value of the acceleration (a) of
theproton is
a
= Eq / m
=
-(-6.60
105i N/C)(1.6*10-19C)
/(1.67*10-27kg)
=
-6.32*1013m/s2i
So magnitude of the acceleration of the particle is a
=6.32*1013m/s2And its direction is
alongnegative x direction
(b)
Distance (S) traveled =7.40cm =...
2.5
ty which will be discussed in chapter 4 2.3 Consider a particle of mass m subject to a one-dimensional potential V(x) that is given by V = 0, x <0; V = 0, 0<x<a; V = Vo, x> Show that bound (E < Vo) states of this system exist only if k cotka = -K where k2 = 2mE/12 and k' = 2m(Vo - E)/h4. 2.4 Show that if Vo = 974/2ma, only one bound state of the system...
6. (20pts) Consider a particle of mass m and energy E approaching the step potential V(x) = { 0x< V.>0 x > 0 from negative values of x. Consider the case E> Vo. a) Classically, what is the probability of reflection? b) Quantum mechanically, what is the probability of reflection? Express your result in terms of the ratio VIE. What is the probability of reflection if E= 2Vo?
Mechanics. Need help with c) and d)
1. A particle of mass m moves in three dimensions, and has position r(t)-(x(t), y(t), z(t)) at time t. The particle has potential energy V(x, y, 2) so that its Lagrangian is given by where i d/dt, dy/dt, dz/dt (a) Writing q(q2.93)-(r, y, z) and denoting by p (p,P2, ps) their associated canonical momenta, show that the Hamiltonian is given by (show it from first principles rather than using the energy) H(q,p)H(g1, 92,9q3,...
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,...
A particle slides along a straight wire so that a--k/v where a is the acceleration, v is the velocity and k-20 m3/s. The particle stars at X 0, t-0, with a speed vo 10 m/s. 2. When the particle is at x = 4 m, the speed v is most nearly A. 2.49 m/s B. 3.46 m/s C. 5.29 m/s D. 6.93 m/s E. 7.50 m/s F. 8.62 m/s G. 8.88 m/s H. 9.13 m/s I 9.81 m/s J. 10.00...
A proton is projected in the positive x direction into
aregion of uniform electric field E = -6.60
105i N/C att = 0. The proton
travels 7.40 cm as it comes to rest.(a)
Formula for calculating the value of the acceleration (a) of
theproton is
a
= Eq / m
=
-(-6.60
105i N/C)(1.6*10-19C)
/(1.67*10-27kg)
=
-6.32*1013m/s2i
So magnitude of the acceleration of the particle is a
=6.32*1013m/s2And its direction is
alongnegative x direction
(b)
Distance (S) traveled =7.40cm =...
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