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rt numpy as np import scipy.integrate as si import matplotlib.

rt numpy as np import scipy.integrate as si import matplotlib.

Database System Concepts
Database System Concepts
7th Edition
ISBN:9780078022159
Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Chapter1: Introduction
Section: Chapter Questions
Problem 1PE
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need help with python by using

import numpy as np
import scipy.integrate as si
import matplotlib.pyplot as plt
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: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
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
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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