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.
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a) What is Schrodinger's equation for a particle of mass m that
is constrained to move...
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) 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
plz help. thnx The state of a quantum mechanical particle, constrained to move on a circle...
plz help. thnx
The state of a quantum mechanical particle, constrained to move on a circle of radius R in the x-y plane, is given by 4. where ф is the angle that the position vector makes with the x-axis a) Find a value of N which makes the above state normalized b) If Lz is measured, what are the possible outcomes and their corresponding probabilities?
Consider a particle of mass m in an infinite spherical potential well of radius a For write down the energies and corresponding eigen functions ψ--(r,0.9). (3 pt) a) ne that at t-o the wave fu...
Consider a particle of mass m in an infinite spherical potential well of radius a For write down the energies and corresponding eigen functions ψ--(r,0.9). (3 pt) a) ne that at t-o the wave function is given by o)-A. Find the normalization constant A function in this basis. Solve for the coeffici You may find useful the integrals in the front of the (6 pt) d) Now consider the finite potential spherical well with V(r)- ing only the radial part...
4. A particle of mass m is constrained to slide without friction on the surface of...
4. A particle of mass m is constrained to slide without friction on the surface of a smooth circular bowl of mass M with inner radius R as shown in the figure. The bottom of the bowl lies on a horizontal table and is free to slide without friction along the table. All motion is constrained to the plane of the page. Assume uniform gravitati acceleration. =T-V- State the Lagrangian for this system. Derive the differential equations of motion for...
JO) A Pi- electron in benzene molecule may be described in quantum com make the assumption...
JO) A Pi- electron in benzene molecule may be described in quantum com make the assumption that benzene is circular. In such a case, the potential energy is constant (1.e. V =0) and Schrodinger equation for a particle of mass me constrained to move on a circle of radius a is: (-h7/8 Tma)dade - Em for 0 SOS 27. Here is the angle that describes the position of the particle (i.e. pi-electron) around the ning a) Show that the solution...
A particle (mass m, charge q) is constrained to move freely along a straight horizontal wire...
A particle (mass m, charge q) is constrained to move freely along a straight horizontal wire of length L. At one end of the wire is a fixed point charge Q1; at the other end of the wire is a fixed point charge Q2. Assume all three charges are negative, and that Q1 = 4Q2. Determine the particle
3. A particle of mass is constrained to move without friction along the x-axis, subject to...
3. A particle of mass is constrained to move without friction along the x-axis, subject to a potential energy siven by Ue) Uo/ constants. Show that for small oscillations about x 0, the particle undergoes simple harmonic motion. What condition on x is required for the oscillations to be "small" (i.e. simple harmonic)? Find the period Tof the oscillations. - 1) where Uo and b are positive
The velocity of a particle constrained to move along the x-axis as a function of time...
The velocity of a particle constrained to move along the x-axis as a function of time t is given by: v(t)=−(18/t0)sin(t/t0). Part A If the particle is at x=1 m when t=0, what is its position at t = 7t0. You will not need the value of t0 to solve any part of this problem. If it is bothering you, feel free to set t0=1 everywhere. Part B Denote instantaneous acceleration of this particle by a(t). Evaluate the expression 1...
4. Consider a double pendulum with identical length, L and mass, m constrained to move in...
4. Consider a double pendulum with identical length, L and mass, m constrained to move in the x-y plane. Using the Cartesian coordinates, x and y write down the kinetic and potential energies of the system in terms of, and θ2. Find the Lagrangian and two corresponding equations for the system. Assume the angles 0, and 02 are both very small so that sin θ θ and cos θ 1 and state the approximate equations
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) 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
plz help. thnx
The state of a quantum mechanical particle, constrained to move on a circle of radius R in the x-y plane, is given by 4. where ф is the angle that the position vector makes with the x-axis a) Find a value of N which makes the above state normalized b) If Lz is measured, what are the possible outcomes and their corresponding probabilities?
Consider a particle of mass m in an infinite spherical potential well of radius a For write down the energies and corresponding eigen functions ψ--(r,0.9). (3 pt) a) ne that at t-o the wave function is given by o)-A. Find the normalization constant A function in this basis. Solve for the coeffici You may find useful the integrals in the front of the (6 pt) d) Now consider the finite potential spherical well with V(r)- ing only the radial part...
4. A particle of mass m is constrained to slide without friction on the surface of a smooth circular bowl of mass M with inner radius R as shown in the figure. The bottom of the bowl lies on a horizontal table and is free to slide without friction along the table. All motion is constrained to the plane of the page. Assume uniform gravitati acceleration. =T-V- State the Lagrangian for this system. Derive the differential equations of motion for...
JO) A Pi- electron in benzene molecule may be described in quantum com make the assumption that benzene is circular. In such a case, the potential energy is constant (1.e. V =0) and Schrodinger equation for a particle of mass me constrained to move on a circle of radius a is: (-h7/8 Tma)dade - Em for 0 SOS 27. Here is the angle that describes the position of the particle (i.e. pi-electron) around the ning a) Show that the solution...
3. A particle of mass is constrained to move without friction along the x-axis, subject to a potential energy siven by Ue) Uo/ constants. Show that for small oscillations about x 0, the particle undergoes simple harmonic motion. What condition on x is required for the oscillations to be "small" (i.e. simple harmonic)? Find the period Tof the oscillations. - 1) where Uo and b are positive
4. Consider a double pendulum with identical length, L and mass, m constrained to move in the x-y plane. Using the Cartesian coordinates, x and y write down the kinetic and potential energies of the system in terms of, and θ2. Find the Lagrangian and two corresponding equations for the system. Assume the angles 0, and 02 are both very small so that sin θ θ and cos θ 1 and state the approximate equations
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