The hydrogenic radial function R(r) are relatively simple for the case l = n-1 (the maximum...
The hydrogenic radial function R(r) are relatively simple for the case l = n-1 (the maximum allowed value for l for given n):
R(r) = Arn-1 er/ab (l = n -1)
(a) Write down the radial schrodinger equation for this case.
(b) Verify that the proposed solution does indeed satisfy this equation if and only if En = -Er/n2
(c) Plot the radial function R(r) for n = 0,1,2, (assume
ab=1)
Homework Answers
a)Let 
. So the radial equation is 
b)Taking 
.
On taking the derivative and comparing the terms we get
Add Answer to:
The hydrogenic radial function R(r) are relatively simple for
the case l = n-1 (the maximum...
From Eq. 13.60 the normalized radial part of the hydrogenic wave function is (n - L...
From Eq. 13.60 the normalized radial part of the hydrogenic wave function is (n - L - 1)! 71/2 Rul(r) = e-ar/2 («r)ʻL?---,(«r), 2n(n + L)! in which « = 2Z/na, = 2Zme?/nh?. Evaluate =S" rRazlar)R_(\n* dr, (b) <**>= $*** Rukar) Radkor»- dr. (a) (r) = The quantity (r) is the average displacement of the electron from the nucleus, whereas <r-) is the average of the reciprocal displacement. ANS. Co [312 – L(L + 1)] 2 1 -?) nao
Radial Functions 1. The radial Schrödinger equation (in atomic units) 1 (d2R 2 dR (1)1 HR =- has ...
Radial Functions 1. The radial Schrödinger equation (in atomic units) 1 (d2R 2 dR (1)1 HR =- has the normalized analytic solutions (radial functions): 2+1 List these functions in 'Tab!eForm, up to n=2 Plot the corresponding radial distributions (r2 R2), also in 'TableForm'. Calculate the maximum probability radius for the 1s state (n=1, 0). This involves finding the location of the maximum of r2R0. d.) Show that the Is Radial function is orthogonal to that of the 2s. DO (R101...
4. Consider the equation N,+1 = N, exp[r(1-N/K)] This equation is sometimes called an analog of...
4. Consider the equation N,+1 = N, exp[r(1-N/K)] This equation is sometimes called an analog of the logistic differential equation (May, 1975). The equation models a single-species population growing in an environment that has a carrying capacity K. By this we mean that the environ- ment can only sustain a maximal population level N = K. The expression reflects a density dependence in the reproductive rate. To verify this observa- tion, consider the following steps: (a) Sketch A as a...
Show that R(r) is a solution of the following differential equation for l = 1, R(r)...
Show that R(r) is a solution of the following differential
equation for l = 1, R(r) = (r/ao) *
e-r/2ao.
What is the eigenvalue? Using this result, calculate the value
of the principal quantum number (n) for this function.
h21(L+1) 2mer2 h2 e2 d dR(r) ]R(r) 4περr ER(r) 2mer2 dr dr
Determine and plot the autocorrelation function rxx[l] of the signal 1, 0≤n≤N−1 x[n] = 0, otherwise...
Determine and plot the autocorrelation function rxx[l] of the
signal 1, 0≤n≤N−1
x[n] = 0, otherwise .
Determine and plot the autocorrelation function r] of the signal x[n] = 0, otherwise
2. Consider the parallel RLC circuit mentioned in class, with C = 1, L = 4, and R = 1 (a) Derive the iin-to v transfer...
2. Consider the parallel RLC circuit mentioned in class, with C = 1, L = 4, and R = 1 (a) Derive the iin-to v transfer function, i.e., the circuit's impedance (b) Compute and plot the step response (c) Plot the magnitude of the frequency response function, G(jw) as a function of Compute, via analysis, the frequency wmar Wwhere maximum gain |G(jw)| is w. maximized (d) Verify your results using MATLAB: Plot the system's response to a step, and to...
Using mathematica please help me solve this For a radial wavefunction of the form Rn() of the one-electron atom graph the following function for n-2, 1-0: 1 ao And n = 2, l=1 Using an angular wa...
Using mathematica please help me solve this
For a radial wavefunction of the form Rn() of the one-electron atom graph the following function for n-2, 1-0: 1 ao And n = 2, l=1 Using an angular wavefunction of the form Y1n(8,0) of the one electron atom graph the following for l = 0 and m' =0; 12. 11 47T And I = 0, mi =0 İS. Cos 47T 13.
For a radial wavefunction of the form Rn() of the one-electron...
3.27 Average distance from the nucleus and atomic radius The maximum in the radial probability distribution...
3.27 Average distance from the nucleus and atomic radius The maximum in the radial probability distribution of an electron in a hydrogen-like atom is given by Equation 3.58, that is, rmax - (n'ao)/Z, for l - n- 1. The average distance F of an electron from the nucleus can be calculated by using the definition of an average and the probability distribution function Pn/(r), that is, Z. elective 2 2n2 in which the right-hand side represents the result of the...
(Real Analysis) Please prove for p=3 case with details. Cantor set and Cantor ternary function Properties of Ck o C is closed Proposition 19 C is closed, uncountable, m(C) 0 p-nary expansion Let r...
(Real Analysis)
Please prove for p=3 case with details.
Cantor set and Cantor ternary function Properties of Ck o C is closed Proposition 19 C is closed, uncountable, m(C) 0 p-nary expansion Let r E (0,1) and p a natural number with p as 1. Then r can be written where a e (0,1,2.. ,p-1) r- p" Proof for p 3 case: HW 36 Cantor set and Cantor ternary function Unique expression when p 3 x E (0, 1), p-3...
1. Suppose that r,., n are a random sample having probability density function Here the parameter...
1. Suppose that r,., n are a random sample having probability density function Here the parameter θ > 0. (a) Determine the log-likelihood, (0), and a 1-dimensional sufficient statistic. (b) Show that P(X, S b:0) for f(r;0) given in (1) (c) Suppose now that because of a recurring computer glitch in storing the observations, only a +1 for f(r; random subset of the x, are observed. For the rest of the observations, it is only known that z; < 1/2....
From Eq. 13.60 the normalized radial part of the hydrogenic wave function is (n - L - 1)! 71/2 Rul(r) = e-ar/2 («r)ʻL?---,(«r), 2n(n + L)! in which « = 2Z/na, = 2Zme?/nh?. Evaluate =S" rRazlar)R_(\n* dr, (b) <**>= $*** Rukar) Radkor»- dr. (a) (r) = The quantity (r) is the average displacement of the electron from the nucleus, whereas <r-) is the average of the reciprocal displacement. ANS. Co [312 – L(L + 1)] 2 1 -?) nao
Radial Functions 1. The radial Schrödinger equation (in atomic units) 1 (d2R 2 dR (1)1 HR =- has the normalized analytic solutions (radial functions): 2+1 List these functions in 'Tab!eForm, up to n=2 Plot the corresponding radial distributions (r2 R2), also in 'TableForm'. Calculate the maximum probability radius for the 1s state (n=1, 0). This involves finding the location of the maximum of r2R0. d.) Show that the Is Radial function is orthogonal to that of the 2s. DO (R101...
4. Consider the equation N,+1 = N, exp[r(1-N/K)] This equation is sometimes called an analog of the logistic differential equation (May, 1975). The equation models a single-species population growing in an environment that has a carrying capacity K. By this we mean that the environ- ment can only sustain a maximal population level N = K. The expression reflects a density dependence in the reproductive rate. To verify this observa- tion, consider the following steps: (a) Sketch A as a...
Show that R(r) is a solution of the following differential
equation for l = 1, R(r) = (r/ao) *
e-r/2ao.
What is the eigenvalue? Using this result, calculate the value
of the principal quantum number (n) for this function.
h21(L+1) 2mer2 h2 e2 d dR(r) ]R(r) 4περr ER(r) 2mer2 dr dr
Determine and plot the autocorrelation function rxx[l] of the
signal 1, 0≤n≤N−1
x[n] = 0, otherwise .
Determine and plot the autocorrelation function r] of the signal x[n] = 0, otherwise
2. Consider the parallel RLC circuit mentioned in class, with C = 1, L = 4, and R = 1 (a) Derive the iin-to v transfer function, i.e., the circuit's impedance (b) Compute and plot the step response (c) Plot the magnitude of the frequency response function, G(jw) as a function of Compute, via analysis, the frequency wmar Wwhere maximum gain |G(jw)| is w. maximized (d) Verify your results using MATLAB: Plot the system's response to a step, and to...
Using mathematica please help me solve this
For a radial wavefunction of the form Rn() of the one-electron atom graph the following function for n-2, 1-0: 1 ao And n = 2, l=1 Using an angular wavefunction of the form Y1n(8,0) of the one electron atom graph the following for l = 0 and m' =0; 12. 11 47T And I = 0, mi =0 İS. Cos 47T 13.
For a radial wavefunction of the form Rn() of the one-electron...
3.27 Average distance from the nucleus and atomic radius The maximum in the radial probability distribution of an electron in a hydrogen-like atom is given by Equation 3.58, that is, rmax - (n'ao)/Z, for l - n- 1. The average distance F of an electron from the nucleus can be calculated by using the definition of an average and the probability distribution function Pn/(r), that is, Z. elective 2 2n2 in which the right-hand side represents the result of the...
(Real Analysis)
Please prove for p=3 case with details.
Cantor set and Cantor ternary function Properties of Ck o C is closed Proposition 19 C is closed, uncountable, m(C) 0 p-nary expansion Let r E (0,1) and p a natural number with p as 1. Then r can be written where a e (0,1,2.. ,p-1) r- p" Proof for p 3 case: HW 36 Cantor set and Cantor ternary function Unique expression when p 3 x E (0, 1), p-3...
1. Suppose that r,., n are a random sample having probability density function Here the parameter θ > 0. (a) Determine the log-likelihood, (0), and a 1-dimensional sufficient statistic. (b) Show that P(X, S b:0) for f(r;0) given in (1) (c) Suppose now that because of a recurring computer glitch in storing the observations, only a +1 for f(r; random subset of the x, are observed. For the rest of the observations, it is only known that z; < 1/2....
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