Determining Intersection Points of Equations in Quantum Mechanics

  • Context: Graduate 
  • Thread starter Thread starter atomqwerty
  • Start date Start date
  • Tags Tags
    Intersection Points
Click For Summary
SUMMARY

The discussion focuses on determining the intersection points of the equations 1-(2/a)x and ±Exp(-x) within the context of quantum mechanics. It is established that these equations cannot be solved algebraically, as they require finding the roots of the combined function 1-(2/a)x ± Exp(-x). Participants recommend using numerical techniques or software tools such as Mathematica or MATLAB for effective resolution of the problem.

PREREQUISITES
  • Understanding of quantum mechanics principles
  • Familiarity with numerical methods for solving equations
  • Proficiency in using Mathematica or MATLAB
  • Knowledge of exponential functions and their properties
NEXT STEPS
  • Explore numerical methods for root-finding, such as the Newton-Raphson method
  • Learn how to implement equation solving in Mathematica
  • Investigate MATLAB's built-in functions for numerical analysis
  • Study the properties of exponential decay functions in mathematical modeling
USEFUL FOR

Students and professionals in quantum mechanics, mathematicians, and anyone involved in numerical analysis or computational physics seeking to solve complex equations.

atomqwerty
Messages
89
Reaction score
0
Hello,
How can I determinate the intersection points of these equations:

1-(2/a)x

and

+- Exp(-x)

It's from an exercise on quantum mechanics where I don't know why the gradient of the exponential is -1.


YThanks
 
Mathematics news on Phys.org
As far as I know, this cannot be solved algebraically. This is equivalent to asking what the roots are of 1-(2/a)x +- Exp(-x). The best I can think of is using mathematica/matlab or a numerical technique (if you've learned any).
 

Similar threads

Undergrad Eccentric anomaly of ellipse-circle intersections
  • · Replies 4 ·
Replies
4
Views
2K
MHB Finding Points of Intersection for Trigonometric Functions
  • · Replies 8 ·
Replies
8
Views
3K
MHB Quadratic equations intersaction point is minimum instead of roots
  • · Replies 2 ·
Replies
2
Views
2K
Undergrad How to establish which side of a square a ray will intersect?
  • · Replies 7 ·
Replies
7
Views
2K
MHB Planes 1 & 2 Intersect: Find Scalar Equations
  • · Replies 1 ·
Replies
1
Views
2K
MHB How Are Tangents to a Circle Found and Their Intersection Point Determined?
  • · Replies 5 ·
Replies
5
Views
2K
High School Invariant under rotation: Banal, obvious, or noteworthy?
  • · Replies 2 ·
Replies
2
Views
2K
Undergrad Family of Circles at Two Points
  • · Replies 2 ·
Replies
2
Views
2K
MHB Where Do the Diagonals of a Parallelogram Intersect?
  • · Replies 8 ·
Replies
8
Views
4K
MHB Quadratic Equation Help: Find 3 Points to Determine Answer
  • · Replies 6 ·
Replies
6
Views
2K