Understanding Time-Independent Schrodinger Equation

Click For Summary
SUMMARY

The time-independent Schrödinger equation (TISE) is a fundamental concept in quantum mechanics that describes the stationary states of a quantum system. It is essential to understand that while the TISE does not explicitly include time, it is used to derive the time-dependent Schrödinger equation (TDSE), which governs the evolution of quantum states over time. The relationship between the two equations is crucial, as solving the TISE allows for the determination of eigenstates, which can then be combined with time-dependent factors to fully describe the dynamics of a quantum system.

PREREQUISITES
  • Understanding of quantum mechanics principles
  • Familiarity with the Schrödinger equation
  • Knowledge of eigenstates and eigenvalues
  • Basic grasp of wave functions
NEXT STEPS
  • Study the derivation of the time-dependent Schrödinger equation
  • Explore the concept of eigenstates and their significance in quantum mechanics
  • Learn about the role of boundary conditions in solving the time-independent Schrödinger equation
  • Investigate applications of the Schrödinger equation in quantum systems
USEFUL FOR

Students and professionals in physics, particularly those focusing on quantum mechanics, theoretical physicists, and anyone interested in the mathematical foundations of quantum systems.

saravanan13
Messages
52
Reaction score
0
In quantum mechanics, time independent Schrödinger equation gives dynamics of system.
How do one claim that this equation is evolution of a system? Since dynamics need time dependency. How do one explain this discrepancy?
Thanks in well advance...
 
Physics news on Phys.org
It's actually the time dependent SE that gives the dynamics. It just turns out that solving the time dependent SE is accomplished by first solving the time independent version, and then the associated time dependence that comes from the time dependent version is rather trivial to attach to the eigenstates of the time independent version.
 

Similar threads

Undergrad Schrödinger equation and classical wave equation
  • · Replies 39 ·
2
Replies
39
Views
4K
Undergrad My problem with time-dependent Schrodinger equation
  • · Replies 6 ·
Replies
6
Views
2K
Undergrad Postulate of only time dependence on |ψ⟩
  • · Replies 2 ·
Replies
2
Views
1K
Undergrad Why the linear combination of eigenfunctions is not a solution of the TISE
  • · Replies 24 ·
Replies
24
Views
3K
Undergrad Schrodinger equation for N particles in a box
  • · Replies 3 ·
Replies
3
Views
2K
Undergrad How to add time variation to a Schrodinger operator?
  • · Replies 11 ·
Replies
11
Views
2K
Undergrad Time-dependent to time-independent Schrödinger equation
  • · Replies 5 ·
Replies
5
Views
2K
Undergrad Time dependence of operators in the Schrödinger picture
  • · Replies 5 ·
Replies
5
Views
2K
Undergrad Wave function using the time dependent Schrodinger equation
  • · Replies 1 ·
Replies
1
Views
2K
Undergrad What is the Meaning of the Schrödinger Equation?
  • · Replies 11 ·
Replies
11
Views
2K