Database System Concepts
7th Edition
ISBN: 9780078022159
Author: Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Publisher: McGraw-Hill Education
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need help with python by using
import numpy as np
import scipy.integrate as si
import matplotlib.pyplot as plt
Transcribed Image Text:Q2. Refer to https://en.wikipedia.org/wiki/Hydrogen_atom
Repeat Q1 for the hydrogen in the 2s state, 2s = W2,0,0-
ymin, ymax= 0.0 489806111.1768066
xinit,xlast= 0.0 1.06e-10
count, Np, A = 1539 3000 0.0519194477847415
I = A*count/Np =
0.026634676713572388
le9
P(r) vs. r/a
175
150
125
100
0.75
0.50
0.25
0.00
6
rla0
integrated value from stochastic method = 0.026634676713572388
Your output should be similar to that as displayed in the sample. integrated value by scipy = 0.026326508671855577
Remark: To answer this question, you have to figure out yourself what is the wave function fo the hydrogen atom in the 2s state from the
wikipedia link.
(1)d
Transcribed Image Text:Stochastic integration
Q1. Refer to https://en.wikipedia.org/wiki/Hydrogen_atom
Read through the wiki page. The radial part of the ground state solution to the 3D Schrodinger equation for hydrogen atom is given by the
express Y1s(r) :
-e-rla0, where r is the position variable measured from the center of the hidrogen atom, and ao the Bohr radius. The
total probability P(r)dr of the electron being in a shell at a distance r and thickness dr is P(r)dr = 4ar² |y1s(r)[² dr.
(i) Use stochastic integration method to calculate the probability of finding an electron in the region 0 < r < 2ao. To this end, you must find
out what is the numerical value for the Bohr radius, ao in Sl unit.
(ii) Use scipy.integrate.quad() to perform the calculation in (i) and display on the screen that the methods in (i) and (ii) return consistent answer
of 20.76.
(iii) Plot the curve of P(r) vs. rla0 for 0 < r< 5a0. Display the stochastic dots in (i) that are bounded between the curve and the r-axis in the
region 0 <r < ao. Your output should be similar to that as displayed in the sample.
Remark: This is a 'tricky' question in the sense that the x-axis is not in SI unit but in ao.
ymin, ymax= 0.0 10213942675.451843
xinit,xlast= 0.0 1.06e-10
count, Np, A = 2148 3000 1.0826779235978954
I = A*count/Np =
0.775197393296093
le10
P(r) vs. r/a
10
0.8
0.6
0.4
0.2
0.0
4
5
6
r/a0
integrated value from stochastic method = 0.775197393296093
integrated value by scipy =
0.7618966944464558
(1)d
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