It's in Mathematical Methods for Physicists 7e, Arfken ch7.6 Other solutions (ODEs).
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It's in Mathematical Methods for Physicists 7e, Arfken ch7.6 Other solutions (ODEs). Please help. Thank you. One solution of Hermite's differential equation 7.6.19 (a) for α = 0 is yi (x) = l...
It's in Mathematical Methods for Physicists 7e, Arfken ch7.6 Other solutions (ODEs). Please help. Thank you....
It's in Mathematical Methods for Physicists 7e, Arfken ch7.6
Other solutions (ODEs).
Please help.
Thank you.
One solution of Hermite's differential equation 7.6.19 (a) for α = 0 is yi (x) = l. Find a second solution, y2(x), using Eq. (7.67). Show that your second solution is equivalent to yodd (Exercise 8.3.3). Find a second solution for α = 1, where yi (x) =x, using Eq. (7.67). Show that your second solution is equivalent to yeven (Exercise 8.3.3) (b)
It's in Mathematical Methods for Physicists 7e, Arfken ch7.7 Inhomogeeous linear ODEs. Please help. Thank you. 7.7.1 If our linear, second-order ODE is inhomogeneous, tha is, of the form of Eq. (...
It's in Mathematical Methods for Physicists 7e, Arfken ch7.7
Inhomogeeous linear ODEs.
Please help.
Thank you.
7.7.1 If our linear, second-order ODE is inhomogeneous, tha is, of the form of Eq. (7.94), the most general solution is where yi and y2 are independent solutions of the homogeneous equation Show that yi(x)2()Fsds W[yi(s), y2()) Wyi(), y2(s) with Wlyxy2x)) the Wronskian of yi(s) and y2(s) Find the general solutions to the following inhomogeneous ODEs:
7.7.1 If our linear, second-order ODE is inhomogeneous,...
7.6.26 It's in Mathematical Methods for Physicists 7e, Arfken Please help. Thank you so much. 7.6.26 (a) Show that...
7.6.26
It's in Mathematical Methods for Physicists 7e, Arfken
Please help.
Thank you so much.
7.6.26 (a) Show that has two solutions: (b) For α 0 the two linearly independent solutions of part (a) reduce to the single solution y o. Using Eq. (7.68) derive a second solution, Verify that y is indeed a solution. (c) Show that the second solution from part (b) may be obtained as a ing case from the two solutions of part (a): lim (...
It's in Mathematical Methods for Physicists 7e, Arfken ch7.4 second order linear ODEs. (singular ...
It's in Mathematical Methods for Physicists 7e, Arfken ch7.4
second order linear ODEs. (singular points)
Please help.
Thank you.
Show that the substitution 7.4.5 a=-l, b=1+1, c=1 converts the hypergeometric equation into Legendre's equation
Show that the substitution 7.4.5 a=-l, b=1+1, c=1 converts the hypergeometric equation into Legendre's equation
9.4.6 It's in Mathematical Methods for Physicists 7e, Arfken ch9.4 Seperation of variables. Please help. Thank you...
9.4.6
It's in Mathematical Methods for Physicists 7e, Arfken ch9.4
Seperation of variables.
Please help.
Thank you so much.
The quantum mechanical angular momentum operator is given by L - i(r x V). Show that 9.4.6 leads to the associated Legendre equation. Hint. Section 8.3 and Exercise 8.3.1 may be helpful.
The quantum mechanical angular momentum operator is given by L - i(r x V). Show that 9.4.6 leads to the associated Legendre equation. Hint. Section 8.3 and Exercise 8.3.1...
9.4.5 It's in Mathematical Methods for Physicists 7e, Arfken ch9.4 Seperation of variables. Please help. Thank you...
9.4.5
It's in Mathematical Methods for Physicists 7e, Arfken ch9.4
Seperation of variables.
Please help.
Thank you so much.
9.4.5 An atomic (quantum mechanical) particle is confined inside a rectangular box of sides a, b, and c. The particle is described by a wave function wave equation that satisfies the Schrödinger 2m The wave function is required to vanish at each surface of the box (but not to be identi- cally zero). This condition imposes constraints on the separation constants...
15.4.1 It's in Mathematical Methods for Physicists 6e, Arfken ch15 Please help. Thank you so much. The one-dimensio...
15.4.1
It's in Mathematical Methods for Physicists 6e, Arfken ch15
Please help.
Thank you so much.
The one-dimensional Fermi age equation for the diffusion of neutrons slowing down in some medium (such as graphite) is 15.4.1 a2q(x, T) aq(x, T) ax2 Here q is the number of neutrons that slow down, falling below some given energy per second per unit volume. The Fermi age, T, is a measure of the energy loss If q (x, 0) S8(x), corresponding to a...
15.4.4 It's in Mathematical Methods for Physicists 6e, Arfken ch15 Please help. Thank you so much. For a point sour...
15.4.4
It's in Mathematical Methods for Physicists 6e, Arfken ch15
Please help.
Thank you so much.
For a point source at the origin, the three-dimensional neutron diffusion equation be 15.4.4 comes -Dv2(r)K2D¢(r) = Q8(r) Apply a three-dimensional Fourier transform. Solve the transformed equation. Trans form the solution back into r-space Hint The following equations are useful 1. Vf(r)eikrdr -kl2f(r)ekr d?r (2)E 1 (2T)E p(r)eikr d2r (2n)E 1 2. Let D(k) -ar 1 4T 3. The Fourier transform of f(r) 1S...
problem 5 l lbout 0 for a general solution to the given differential equation u, y(0) = 0, V,(0) = 1 . Your answer should include a grneral formula for the ncients. (Find a recursive relation. If...
problem 5
l lbout 0 for a general solution to the given differential equation u, y(0) = 0, V,(0) = 1 . Your answer should include a grneral formula for the ncients. (Find a recursive relation. If possible find Vi and 1,2). 3: Chebyshev's equation i(y + p'y-0, where p is a constant. Find two linearly Independert series solutions yi and ya. (Hint: find the series solution to the differential equation at z-0 to factor ao and ai as we...
Consider differential equation (x - 1)y" – xy' + y = 0. a). Show that yi...
Consider differential equation (x - 1)y" – xy' + y = 0. a). Show that yi = el is a solution of this equation. Use the method of reduction of order to find second linearly independent solution y2 of this equation. (2P.) b). Find solution of the initial value problem (1P.) y(1) = 0, y'(1) = 1. c). Find solution of the initial value problem (1P.) y(1) = 0, y'(1) = 0. d). Does your answer in b) and c)...
It's in Mathematical Methods for Physicists 7e, Arfken ch7.6
Other solutions (ODEs).
Please help.
Thank you.
One solution of Hermite's differential equation 7.6.19 (a) for α = 0 is yi (x) = l. Find a second solution, y2(x), using Eq. (7.67). Show that your second solution is equivalent to yodd (Exercise 8.3.3). Find a second solution for α = 1, where yi (x) =x, using Eq. (7.67). Show that your second solution is equivalent to yeven (Exercise 8.3.3) (b)
It's in Mathematical Methods for Physicists 7e, Arfken ch7.7
Inhomogeeous linear ODEs.
Please help.
Thank you.
7.7.1 If our linear, second-order ODE is inhomogeneous, tha is, of the form of Eq. (7.94), the most general solution is where yi and y2 are independent solutions of the homogeneous equation Show that yi(x)2()Fsds W[yi(s), y2()) Wyi(), y2(s) with Wlyxy2x)) the Wronskian of yi(s) and y2(s) Find the general solutions to the following inhomogeneous ODEs:
7.7.1 If our linear, second-order ODE is inhomogeneous,...
7.6.26
It's in Mathematical Methods for Physicists 7e, Arfken
Please help.
Thank you so much.
7.6.26 (a) Show that has two solutions: (b) For α 0 the two linearly independent solutions of part (a) reduce to the single solution y o. Using Eq. (7.68) derive a second solution, Verify that y is indeed a solution. (c) Show that the second solution from part (b) may be obtained as a ing case from the two solutions of part (a): lim (...
It's in Mathematical Methods for Physicists 7e, Arfken ch7.4
second order linear ODEs. (singular points)
Please help.
Thank you.
Show that the substitution 7.4.5 a=-l, b=1+1, c=1 converts the hypergeometric equation into Legendre's equation
Show that the substitution 7.4.5 a=-l, b=1+1, c=1 converts the hypergeometric equation into Legendre's equation
9.4.6
It's in Mathematical Methods for Physicists 7e, Arfken ch9.4
Seperation of variables.
Please help.
Thank you so much.
The quantum mechanical angular momentum operator is given by L - i(r x V). Show that 9.4.6 leads to the associated Legendre equation. Hint. Section 8.3 and Exercise 8.3.1 may be helpful.
The quantum mechanical angular momentum operator is given by L - i(r x V). Show that 9.4.6 leads to the associated Legendre equation. Hint. Section 8.3 and Exercise 8.3.1...
9.4.5
It's in Mathematical Methods for Physicists 7e, Arfken ch9.4
Seperation of variables.
Please help.
Thank you so much.
9.4.5 An atomic (quantum mechanical) particle is confined inside a rectangular box of sides a, b, and c. The particle is described by a wave function wave equation that satisfies the Schrödinger 2m The wave function is required to vanish at each surface of the box (but not to be identi- cally zero). This condition imposes constraints on the separation constants...
15.4.1
It's in Mathematical Methods for Physicists 6e, Arfken ch15
Please help.
Thank you so much.
The one-dimensional Fermi age equation for the diffusion of neutrons slowing down in some medium (such as graphite) is 15.4.1 a2q(x, T) aq(x, T) ax2 Here q is the number of neutrons that slow down, falling below some given energy per second per unit volume. The Fermi age, T, is a measure of the energy loss If q (x, 0) S8(x), corresponding to a...
15.4.4
It's in Mathematical Methods for Physicists 6e, Arfken ch15
Please help.
Thank you so much.
For a point source at the origin, the three-dimensional neutron diffusion equation be 15.4.4 comes -Dv2(r)K2D¢(r) = Q8(r) Apply a three-dimensional Fourier transform. Solve the transformed equation. Trans form the solution back into r-space Hint The following equations are useful 1. Vf(r)eikrdr -kl2f(r)ekr d?r (2)E 1 (2T)E p(r)eikr d2r (2n)E 1 2. Let D(k) -ar 1 4T 3. The Fourier transform of f(r) 1S...
problem 5
l lbout 0 for a general solution to the given differential equation u, y(0) = 0, V,(0) = 1 . Your answer should include a grneral formula for the ncients. (Find a recursive relation. If possible find Vi and 1,2). 3: Chebyshev's equation i(y + p'y-0, where p is a constant. Find two linearly Independert series solutions yi and ya. (Hint: find the series solution to the differential equation at z-0 to factor ao and ai as we...
Consider differential equation (x - 1)y" – xy' + y = 0. a). Show that yi = el is a solution of this equation. Use the method of reduction of order to find second linearly independent solution y2 of this equation. (2P.) b). Find solution of the initial value problem (1P.) y(1) = 0, y'(1) = 1. c). Find solution of the initial value problem (1P.) y(1) = 0, y'(1) = 0. d). Does your answer in b) and c)...
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