Time derivative of schrodinger equation

Click For Summary
SUMMARY

The Time-Dependent Schrödinger Equation (TDSE) is defined with a first derivative in time to ensure that wave functions remain complex, which is essential for the mathematical framework of quantum mechanics. This requirement can be rationalized through Noether's theorem, linking energy conservation to time translations. If the TDSE were a second-order derivative in time, it would lead to non-physical solutions, such as instabilities in the wave function. The necessity for complex wave functions is rooted in the fundamental principles of quantum mechanics, ensuring the proper representation of quantum states.

PREREQUISITES
  • Understanding of quantum mechanics principles
  • Familiarity with the Schrödinger equation
  • Knowledge of Noether's theorem
  • Basic concepts of wave functions and their properties
NEXT STEPS
  • Explore the implications of Noether's theorem in quantum mechanics
  • Research the mathematical properties of complex wave functions
  • Study the differences between first-order and second-order differential equations in physics
  • Investigate the physical interpretations of wave function collapse
USEFUL FOR

Quantum physicists, students of quantum mechanics, and researchers interested in the mathematical foundations of quantum theory.

geet89
Messages
3
Reaction score
0
Why is the TDSE first derivative in time. Now I know that it is required so that the wave functions are complex... but is there any physical interpretation for this requirment??
 
Physics news on Phys.org
Ultimately, it's a postulate of QM. But you can rationalize it in various ways, for instance by Noether's theorem, energy is the conserved quantity under time translations.
 
Can u give me some examples of what would happen if it were a second order derivative in time... and why should the wave functions always be complex?
 

Similar threads

Undergrad Schrödinger equation and classical wave equation
  • · Replies 39 ·
2
Replies
39
Views
4K
Undergrad Postulate of only time dependence on |ψ⟩
  • · Replies 2 ·
Replies
2
Views
1K
Undergrad How to derive Schrodinger's equation?
  • · Replies 9 ·
Replies
9
Views
4K
Undergrad Derivation of Schrodinger equation (chicken and egg problem?)
  • · Replies 17 ·
Replies
17
Views
3K
Undergrad Time dependence of operators in the Schrödinger picture
  • · Replies 5 ·
Replies
5
Views
2K
Undergrad My problem with time-dependent Schrodinger equation
  • · Replies 6 ·
Replies
6
Views
2K
Undergrad Conventional description of the matter wave
  • · Replies 1 ·
Replies
1
Views
1K
High School Particle Function? Particle Equation?
  • · Replies 21 ·
Replies
21
Views
2K
Graduate Schrodinger equation/Madelung equation phase transformation
  • · Replies 32 ·
2
Replies
32
Views
3K
Undergrad Klein-Gordon equation in the nonrelativistic limit
  • · Replies 3 ·
Replies
3
Views
1K