What is the Schrodinger Equation?

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SUMMARY

Schrödinger's Equation is a fundamental equation in quantum mechanics that describes the behavior of atomic and subatomic systems, particularly electrons and atoms. It serves as a quantum analog to Newton's second law of motion (F=ma) in classical mechanics. The equation is a partial differential equation where the wavefunction is the unknown variable, and it is essential for understanding the wave-mechanical nature of particles. There are two variants of the equation, which are typically introduced in undergraduate physics courses, often in the second year of study.

PREREQUISITES
  • Basic understanding of quantum mechanics
  • Familiarity with classical mechanics concepts such as kinematics and dynamics
  • Knowledge of Hamiltonian mechanics
  • Experience with differential equations
NEXT STEPS
  • Study the mathematical formulation of Schrödinger's Equation
  • Learn about wavefunctions and their physical interpretations
  • Explore the differences between time-dependent and time-independent Schrödinger equations
  • Investigate applications of Schrödinger's Equation in quantum chemistry
USEFUL FOR

Students in high school and undergraduate programs, particularly those studying physics or chemistry, as well as educators seeking to clarify the concepts of quantum mechanics and Schrödinger's Equation.

Dynamite
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So I've been looking online @ Schrödinger's Equation, but I still can't get a good grasp of what it's all about...
All I know so far is that its part of quantum mechanics and that its solutions describe atomic and subatomic systems, electrons and atoms.. <---but what does that actually mean?

And I read that there were 2 variants...
(And the simple English definition on Wikipedia is insufficient)

So.. what is the equation all about?
 
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Think Newtonian kinematics, then dynamics; then have another look.
 
.. I'm still as confused as I started out to begin with...
 
Well, the wave-mechanical nature of classical objects, is used to formulate a wave-machanical description of "an electron's position and momentum' = kinematic and dynamic properties.

Start with linear motion (kinematics and dynamics), go through harmonic motion, end up with Schrödinger. It's about one undergrad Physics book worth (unless you're a quick study).
You aren't usually introduced to the quantum and Schrödinger, until 2nd year, btw.
At least in Chem or Phys you aren't (it's for the bigger kids)...
 
HAHA. O goodness. That's great. Because here I am sitting in high school trying to make some sense out of this. Thanks for your help!
 
um...


Simply speaking, Schrödinger's equation is corresponding to "F=ma" at Newton mechanics.
In other word, more difficultly say, it also corresponds to time generation equation at hamilton mechanics. Hamiltonian in Schrödinger's equation undertakes as time transform generator.
 
it is a partially differential equation in which the unknown variable is the wavefunction
 

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