Consider Schrödinger’s time-dependent equation for an electron, with a potential that is uniform and constant at...
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Consider Schrödinger’s time-dependent equation for an
electron, with a potential that
is uniform and constant at...
2. [16 points] What is the solution of the time-dependent Schrödinger Equation Ψ(x, t) for the...
2. [16 points] What is the solution of the time-dependent Schrödinger Equation Ψ(x, t) for the solution of the time-independent Schrödinger Equation Ψ(x) = ,in (m) in the particle in the box model? Write ω =-explicitly in terms of the parameters of the problem. Explicily show that W,(Cx.t) solves the time-dependent Schrödinger Equation 2
3. /15 pts] Imagine solving the SE for a particular potential well and finding two stationary sol...
3. /15 pts] Imagine solving the SE for a particular potential well and finding two stationary solutions. The first solution i(x) has an energy Eo and of the (unnormalized) form: ψ1(x) = exp(-x2/2) The second solution U2(2) has an energy 3F0 and of the (unnormalized) form ψ2(x) = V2x exp(-x2/2 Consider the quantum state ψ(r state at t = 0 is shown below: t)-V1 (a , t) + 2( , t A crude sketch of the PDF for this t...
2. (i) The governing equation of motion for a single electron of mass m and charge -e moving with velocity y in uniform time-independent magnetic and electric fields is given by mayx B where B- (B, 0...
2. (i) The governing equation of motion for a single electron of mass m and charge -e moving with velocity y in uniform time-independent magnetic and electric fields is given by mayx B where B- (B, 0,0) di dr (a) Suppose the electron initially moves with velocity y (0,vo 0) in an electric field parallel to the magnetic field E-E-(E,00) By taking vf)-v +vi, where y i0, obtain v, and show that the speed vis constant. Describe (in words) the...
A. Write down the differential equation describing the circuit for an arbitrary time-dependent voltage V (t),...
A. Write down the differential equation describing the circuit for an arbitrary time-dependent voltage V (t), in terms of the inductance L, capacitance C and resistance R of the circuit. B. Determine an analytic solution when the voltage is switched off [V(t) = ol. First, express your solution in terms of arbitrary coefficients as appropriate. Then, determine those coefficients for the initial conditions where the current is given by I(に0)-10 and satisfies I'(t = 0) = 0. C. Determine the...
A. Write down the differential equation describing the circuit for an arbitrary time-dependent voltage V (t),...
A. Write down the differential equation describing the circuit for an arbitrary time-dependent voltage V (t), in terms of the inductance L, capacitance C and resistance R of the circuit. B. Determine an analytic solution when the voltage is switched off [V(t) = ol. First, express your solution in terms of arbitrary coefficients as appropriate. Then, determine those coefficients for the initial conditions where the current is given by I(に0)-10 and satisfies I'(t = 0) = 0. C. Determine the...
3. The normalized solution of the time-dependent Schrödinger equation in the one-dimensional syst...
3. The normalized solution of the time-dependent Schrödinger equation in the one-dimensional system is given by where α and β are constants. If we consider an operator A that contains the time as a parameter, the following relation is established. dt eaueof da of the system? What is the value dt
3. The normalized solution of the time-dependent Schrödinger equation in the one-dimensional system is given by where α and β are constants. If we consider an operator A that...
Question 21 Consider a free electron in one dimension (i.e. an electron free to move along...
Question 21 Consider a free electron in one dimension (i.e. an electron free to move along say the x-direction on (a) The time-independent Schrödinger equation is Αψη (x)-Εηψη (x), where is the Hamiltonian (total energy) operator, and ψη (x) are the electron wave functions associated with energies En Assuming the electron's energy entirely comprises kinetic energy (as it is 'free' there is no potential energy term), write down the Schrödinger equation given that the momentum operator in one- dimension is...
Understand how to find the equation of motion of a particle undergoing uniform circular motion. Consider...
Understand how to find the equation of motion of a particle undergoing uniform circular motion. Consider a particle--the small red block in the figure--that is constrained to move in a circle of radius R. We can specify its position solely by θ(t), the angle that the vector from the origin to the block makes with our chosen reference axis at time t. Following the standard conventions we measure θ(t) in the counterclockwise direction from the positive x axis. (Figure 1)...
Consider a Sinusoidally Driven LC Electrical Circuit, which Contains an Electric Potential Oscill...
Consider a Sinusoidally Driven LC Electrical Circuit, which Contains an Electric Potential Oscillator, E E, cos(or), an Inductor, L, and a Capacitor, C. Note that an Oscillating Charge,g).Forms on the Capacitor Plates, as well as an Oscillating Current, I(). throughout the Circuit, which is Associated with the Driven Frequency, ω , as Shown. 1. 1(6) gt) E(r) Recall that the Electric Potential Over an Inductor is Given by E , and the dl dr Electric Potential Over a Capacitor is...
Learning Goal: To understand the application of the general harmonic equation to the kinematics of a...
Learning Goal:
To understand the application of the general harmonic equation
to the kinematics of a spring oscillator.
One end of a spring with spring constant k is attached to the
wall. The other end is attached to a block of mass m. The block
rests on a frictionless horizontal surface. The equilibrium
position of the left side of the block is defined to be x=0. The
length of the relaxed spring is L. (Figure 1)
The block is slowly...
2. [16 points] What is the solution of the time-dependent Schrödinger Equation Ψ(x, t) for the solution of the time-independent Schrödinger Equation Ψ(x) = ,in (m) in the particle in the box model? Write ω =-explicitly in terms of the parameters of the problem. Explicily show that W,(Cx.t) solves the time-dependent Schrödinger Equation 2
3. /15 pts] Imagine solving the SE for a particular potential well and finding two stationary solutions. The first solution i(x) has an energy Eo and of the (unnormalized) form: ψ1(x) = exp(-x2/2) The second solution U2(2) has an energy 3F0 and of the (unnormalized) form ψ2(x) = V2x exp(-x2/2 Consider the quantum state ψ(r state at t = 0 is shown below: t)-V1 (a , t) + 2( , t A crude sketch of the PDF for this t...
2. (i) The governing equation of motion for a single electron of mass m and charge -e moving with velocity y in uniform time-independent magnetic and electric fields is given by mayx B where B- (B, 0,0) di dr (a) Suppose the electron initially moves with velocity y (0,vo 0) in an electric field parallel to the magnetic field E-E-(E,00) By taking vf)-v +vi, where y i0, obtain v, and show that the speed vis constant. Describe (in words) the...
A. Write down the differential equation describing the circuit for an arbitrary time-dependent voltage V (t), in terms of the inductance L, capacitance C and resistance R of the circuit. B. Determine an analytic solution when the voltage is switched off [V(t) = ol. First, express your solution in terms of arbitrary coefficients as appropriate. Then, determine those coefficients for the initial conditions where the current is given by I(に0)-10 and satisfies I'(t = 0) = 0. C. Determine the...
A. Write down the differential equation describing the circuit for an arbitrary time-dependent voltage V (t), in terms of the inductance L, capacitance C and resistance R of the circuit. B. Determine an analytic solution when the voltage is switched off [V(t) = ol. First, express your solution in terms of arbitrary coefficients as appropriate. Then, determine those coefficients for the initial conditions where the current is given by I(に0)-10 and satisfies I'(t = 0) = 0. C. Determine the...
3. The normalized solution of the time-dependent Schrödinger equation in the one-dimensional system is given by where α and β are constants. If we consider an operator A that contains the time as a parameter, the following relation is established. dt eaueof da of the system? What is the value dt
3. The normalized solution of the time-dependent Schrödinger equation in the one-dimensional system is given by where α and β are constants. If we consider an operator A that...
Question 21 Consider a free electron in one dimension (i.e. an electron free to move along say the x-direction on (a) The time-independent Schrödinger equation is Αψη (x)-Εηψη (x), where is the Hamiltonian (total energy) operator, and ψη (x) are the electron wave functions associated with energies En Assuming the electron's energy entirely comprises kinetic energy (as it is 'free' there is no potential energy term), write down the Schrödinger equation given that the momentum operator in one- dimension is...
Consider a Sinusoidally Driven LC Electrical Circuit, which Contains an Electric Potential Oscillator, E E, cos(or), an Inductor, L, and a Capacitor, C. Note that an Oscillating Charge,g).Forms on the Capacitor Plates, as well as an Oscillating Current, I(). throughout the Circuit, which is Associated with the Driven Frequency, ω , as Shown. 1. 1(6) gt) E(r) Recall that the Electric Potential Over an Inductor is Given by E , and the dl dr Electric Potential Over a Capacitor is...
Learning Goal:
To understand the application of the general harmonic equation
to the kinematics of a spring oscillator.
One end of a spring with spring constant k is attached to the
wall. The other end is attached to a block of mass m. The block
rests on a frictionless horizontal surface. The equilibrium
position of the left side of the block is defined to be x=0. The
length of the relaxed spring is L. (Figure 1)
The block is slowly...
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