Homework Answers
3. (i) Find the kinetic energy of a particle of mass m with position given by...
3. (i) Find the kinetic energy of a particle of mass m with position given by the coordinates (s, u, v), related to the ordinary Cartesian coordinates by y z = 2s + 3 + u = 2u + v = 0+03 (ii) Find the kinetic energy of a particle of mass m whose position is given in cylindrical coordinates = = r cos r sine y (iii) Find the kinetic energy of a particle of mass m with position...
Free quantum particle. In Quantum Mechanics, is the time-independent Schrodinger's equation for a free particle in...
Free quantum particle. In Quantum Mechanics, is the time-independent Schrodinger's equation for a free particle in one dimension. In this equation. is the wavefnnction of the particle, m is its mass. E is its (kinetic) energy, while is the fundamental Planck constant.
3) A particle of mass m is constrained to move on the inside surface of a...
3) A particle of mass m is constrained to move on the inside surface of a smooth cone of half- angle a. The particle is subject to a gravitational force. Determine a set of generalized coordinates and determine the constrains. Find Lagrange's equations of motion
a) What is Schrodinger's equation for a particle of mass m that is constrained to move...
a) What is Schrodinger's equation for a particle of mass m that is constrained to move in a circle of radius R, so that psi depends only on phi? b) Solve this equation for psi and evaluate the normalization constant. (Hint: review the solution of Schrodinger's equation for the hydrogen atom) c) Find the possible energies of the particle. d)Find the possible angular momenta of the particle.
2) A particle of mass m at rest in the Home frame decays into two particles of mass that move apa...
2) A particle of mass m at rest in the Home frame decays into two particles of mass that move apart in opposite directions at the same speed. Let event A be the detection of one of the particles at a distance of 10 m from the original particle, and event B be the detection of the second particle at a distance of 20 m from the original particle. a) What is the speed of each of the decay particles,...
7. The kinetic energy, k, of a particle of mass m is given below, where the...
7. The kinetic energy, k, of a particle of mass m is given below, where the velocity, v, of the particle is constrained to [-1,1] Suppose that a particular particle is known to have mass m - 2 and that the probability that its velocity is in [a,b] is given below. Let K denote the random variable that characterizes the particle's kinetic energy. What is the probability that the kinetic energy is greater than one half? That is, find P[K...
the ns is supposed to be m Assume that a free particle of mass m is...
the ns is supposed to be m
Assume that a free particle of mass m is in state with the following wavefunction: b(,t)= Ae' (2020 - 1944). Use the Born interpretation and the Uncertainty Principle to determine what is known about the position, momentum and energy of the particle in this state. Briefly explain your reasoning and give specific values, where possible.
An alpha particle (m = 4.002602 u) is moving at 3.60 times 10^2 m/s. a) Find...
An alpha particle (m = 4.002602 u) is moving at 3.60 times 10^2 m/s. a) Find its mass in kilograms. (6.64 times 10^-27 kg) b) Find its kinetic energy. (4.30 times 10^-22 J) c) Find its kinetic energy in MeV. (2.69 times 10^-9 MeV) d) Find its momentum. (2.39 times 10^-24 kg. m/s) e) Find its deBroglie wavelength (2.77 times 10^-10 m = 0.277 nm) A stationary nucleus of protactinium-231 (m = 231.035879 u) decays by alpha radiation to a...
The mass are particle Poition anc velocity ot each iloe2e + e.1 M + 3M M-BM...
The mass are particle Poition anc velocity ot each iloe2e + e.1 M + 3M M-BM ex For Kinetic eer ay a) Find he total kinetic energ To with respect to O ) Fired the kinetic energy"Tia f the center af mass about O Find the kinelic eherqy T ahgut the aShou that To Tn + Ta center
The mass are particle Poition anc velocity ot each iloe2e + e.1 M + 3M M-BM ex For Kinetic eer ay a)...
A particle of mass m is constrained to move along the x-axis and is subjected to...
A particle of mass m is constrained to move along the x-axis and
is subjected to a force given by
. Assuming the particle had an initial velocity of Vo and was at
the origin at t = 0, find an equation for the particle's velocity
and set up the integral from which the position equation as a
function of time could be determined. NOTE: You do not need to
evaluate the integral for the position as a function of...
3. (i) Find the kinetic energy of a particle of mass m with position given by the coordinates (s, u, v), related to the ordinary Cartesian coordinates by y z = 2s + 3 + u = 2u + v = 0+03 (ii) Find the kinetic energy of a particle of mass m whose position is given in cylindrical coordinates = = r cos r sine y (iii) Find the kinetic energy of a particle of mass m with position...
Free quantum particle. In Quantum Mechanics, is the time-independent Schrodinger's equation for a free particle in one dimension. In this equation. is the wavefnnction of the particle, m is its mass. E is its (kinetic) energy, while is the fundamental Planck constant.
3) A particle of mass m is constrained to move on the inside surface of a smooth cone of half- angle a. The particle is subject to a gravitational force. Determine a set of generalized coordinates and determine the constrains. Find Lagrange's equations of motion
2) A particle of mass m at rest in the Home frame decays into two particles of mass that move apart in opposite directions at the same speed. Let event A be the detection of one of the particles at a distance of 10 m from the original particle, and event B be the detection of the second particle at a distance of 20 m from the original particle. a) What is the speed of each of the decay particles,...
7. The kinetic energy, k, of a particle of mass m is given below, where the velocity, v, of the particle is constrained to [-1,1] Suppose that a particular particle is known to have mass m - 2 and that the probability that its velocity is in [a,b] is given below. Let K denote the random variable that characterizes the particle's kinetic energy. What is the probability that the kinetic energy is greater than one half? That is, find P[K...
the ns is supposed to be m
Assume that a free particle of mass m is in state with the following wavefunction: b(,t)= Ae' (2020 - 1944). Use the Born interpretation and the Uncertainty Principle to determine what is known about the position, momentum and energy of the particle in this state. Briefly explain your reasoning and give specific values, where possible.
An alpha particle (m = 4.002602 u) is moving at 3.60 times 10^2 m/s. a) Find its mass in kilograms. (6.64 times 10^-27 kg) b) Find its kinetic energy. (4.30 times 10^-22 J) c) Find its kinetic energy in MeV. (2.69 times 10^-9 MeV) d) Find its momentum. (2.39 times 10^-24 kg. m/s) e) Find its deBroglie wavelength (2.77 times 10^-10 m = 0.277 nm) A stationary nucleus of protactinium-231 (m = 231.035879 u) decays by alpha radiation to a...
The mass are particle Poition anc velocity ot each iloe2e + e.1 M + 3M M-BM ex For Kinetic eer ay a) Find he total kinetic energ To with respect to O ) Fired the kinetic energy"Tia f the center af mass about O Find the kinelic eherqy T ahgut the aShou that To Tn + Ta center
The mass are particle Poition anc velocity ot each iloe2e + e.1 M + 3M M-BM ex For Kinetic eer ay a)...
A particle of mass m is constrained to move along the x-axis and
is subjected to a force given by
. Assuming the particle had an initial velocity of Vo and was at
the origin at t = 0, find an equation for the particle's velocity
and set up the integral from which the position equation as a
function of time could be determined. NOTE: You do not need to
evaluate the integral for the position as a function of...
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