12345 6 def f(x): return math.sqrt(-x/(x+1)) def g(x): return math.tan (math.sqrt(2*(x + 1))) xs = np.linspace (-0.999,-0.1, 100) fx = [f(x) for x in xs] 7 8 gx [g(x) for x in xs] 9 10 plt.plot(xs,fx) plt.plot(xs, gx) 11 plt.grid 12 ✓ 0.0s 30 25 20 15 10 10 5 0 -1.0 -0.8 -0.6 -0.4 -0.2 Problem 3 In quantum physics, when finding a bound state for a finite potential well one would end up with the following equation(Yes E is negative): -E = tan 2m √ E + Vo E+Vo ħ² a The goal is to find all Energy(Ę) that satisfy this equation. For simplicity, let = 1 Vo • m = 1 • a = 1 • ħ = 1(Yes this is called natural unit) -E E+1 = tan √2(E+1) Find the value for E € (−1.0, 0) which satisfy the equation above). Make sure you accuracy is < ±10–4

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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%matplotlib inline
import math
import numpy as np
from matplotlib import pyplot as plt
 
 
def f(x):
    return math.sqrt(-x/(x+1))
def g(x):
    return math.tan(math.sqrt(2*(x + 1)))

xs = np.linspace(-0.999,-0.1, 100)
fx = [f(x) for x in xs]
gx = [g(x) for x in xs]
plt.plot(xs,fx)
plt.plot(xs,gx)
plt.grid
12345
6
def f(x):
return math.sqrt(-x/(x+1))
def g(x):
return math.tan (math.sqrt(2*(x + 1)))
xs = np.linspace (-0.999,-0.1, 100)
fx = [f(x) for x in xs]
7
8
gx [g(x) for x in xs]
9
10
plt.plot(xs,fx)
plt.plot(xs, gx)
11 plt.grid
12
✓ 0.0s
<function matplotlib.pyplot.grid(visible=None, which='major', axis='both', **kwargs)>
30
25
20
15
10
10
5
0
-1.0
-0.8
-0.6
-0.4
-0.2
Transcribed Image Text:12345 6 def f(x): return math.sqrt(-x/(x+1)) def g(x): return math.tan (math.sqrt(2*(x + 1))) xs = np.linspace (-0.999,-0.1, 100) fx = [f(x) for x in xs] 7 8 gx [g(x) for x in xs] 9 10 plt.plot(xs,fx) plt.plot(xs, gx) 11 plt.grid 12 ✓ 0.0s <function matplotlib.pyplot.grid(visible=None, which='major', axis='both', **kwargs)> 30 25 20 15 10 10 5 0 -1.0 -0.8 -0.6 -0.4 -0.2
Problem 3
In quantum physics, when finding a bound state for a finite potential well one would end up with the following equation(Yes E is negative):
-E
= tan 2m
√ E + Vo
E+Vo
ħ²
a
The goal is to find all Energy(Ę) that satisfy this equation. For simplicity, let
= 1
Vo
• m = 1
• a = 1
•
ħ = 1(Yes this is called natural unit)
-E
E+1
=
tan √2(E+1)
Find the value for E € (−1.0, 0) which satisfy the equation above). Make sure you accuracy is < ±10–4
Transcribed Image Text:Problem 3 In quantum physics, when finding a bound state for a finite potential well one would end up with the following equation(Yes E is negative): -E = tan 2m √ E + Vo E+Vo ħ² a The goal is to find all Energy(Ę) that satisfy this equation. For simplicity, let = 1 Vo • m = 1 • a = 1 • ħ = 1(Yes this is called natural unit) -E E+1 = tan √2(E+1) Find the value for E € (−1.0, 0) which satisfy the equation above). Make sure you accuracy is < ±10–4
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