Problem 2.55 Find the ground state energy of the harmonic oscillator, to five significant digits, by the "wag-the-dog" method. That is, solve Equation 2.73 numerically, varying K until you get a wave function that goes to zero at large E. In Mathematica, appropriate input code would be Plot[ Evaluate[ u[x] /. NDSolve[ {w/[x] -(x² - K)*u[x] == 0, u[0] == 1, w[0] == 0}, u[x], {x, 0, b} ] ], {x, a, b}, PlotRange -> {c, d} (Here (a, b) is the horizontal range of the graph, and (c, d) is the vertical range-start with a = 0, b = 10, c = – 10, d = 10.) We know that the 2n + 1, so you might start with a “guess" of K = 0.9. Notice what the "tail" of the wave function does. Now try K = 1.1, and note correct solution is K = %3D that the tail flips over. Somewhere in between those values lies the correct solution. Zero in on it by bracketing K tighter and tighter. As you do so, you may want to adjust a, b, c, and d, to zero in on the cross-over point. d²y (2.73) where Kis the energy, in units of (1/2) hw:

Problem 2.55 Find the ground state energy of the harmonic oscillator, to five significant digits, by the "wag-the-dog" method. That is, solve Equation 2.73 numerically, varying K until you get a wave function that goes to zero at large E. In Mathematica, appropriate input code would be Plot[ Evaluate[ u[x] /. NDSolve[ {w/[x] -(x² - K)*u[x] == 0, u[0] == 1, w[0] == 0}, u[x], {x, 0, b} ] ], {x, a, b}, PlotRange -> {c, d} (Here (a, b) is the horizontal range of the graph, and (c, d) is the vertical range-start with a = 0, b = 10, c = – 10, d = 10.) We know that the 2n + 1, so you might start with a “guess" of K = 0.9. Notice what the "tail" of the wave function does. Now try K = 1.1, and note correct solution is K = %3D that the tail flips over. Somewhere in between those values lies the correct solution. Zero in on it by bracketing K tighter and tighter. As you do so, you may want to adjust a, b, c, and d, to zero in on the cross-over point. d²y (2.73) where Kis the energy, in units of (1/2) hw:

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

See similar textbooks

Similar questions

What is AND, OR logic circuit? How we can investigate AND, OR logic circuit? What is the result alalysis of the experiment of AND, OR logic circuit?
Develop a truth table for the standard POS expressions
COMP Q3
i need the answer quickly
Please help me solve problems 13,14 and 15 below. Simplify the following expressions using Boolean Algebra. Please provide a clear and readable solution. Thanks in advance!!! The course subject is Logic Circuits and Switching Theory.
i need the answer quickly
Please help me solve problems 10,11 and 12 below. Simplify the following expressions using Boolean Algebra. Please provide a clear and readable solution. Thanks in advance!!! The course subject is Logic Circuits and Switching Theory.
Q. Explain The n-body problem?
Q.9: Prove the following by use of a truth table: A BA + A BC +ABC=A B+ AC Q.10: Draw the circuit diagrams of the following: (i) F = X YZ+ XY Z+ X YZ (ii) F = AB +(AB+A B)
Answer the following problems. Show your complete solution. 1. Simplify the given SOP and POS expressions using Boolean Algebra (a) F = abc + abc + abc + abc + abc (b) G=(a+b+c)(a+b+c)(a+b+c) 2. Make a truth table for F and G expressions of problem 1, compairing the output of original and simplified expressions. 3. Create the logic diagram of the original and simplified of F and G in problem 1.
State the generalized pigeonhole principle.
Computer Science 1. Prove that (A + B) (A + C) = A + BC