What kind of differential equation is the Schrodinger equation?

In summary, the Schrodinger equation is a mathematical equation that describes the time evolution of the wave function of a quantum system. It represents the fundamental equation of quantum mechanics and is a partial differential equation involving the system's energy and potential. It is a second-order partial differential equation and is important because it is the foundation of quantum mechanics and has successfully predicted the behavior of particles at the microscopic level.
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Does it have an easy classification (elliptic, hyperbolic, parabolic, for example)? Or does the fact that it has an "i" in it make this impossible?
 
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At least for time-independent potentials, the Schrodinger equation is formally equivalent to a diffusion equation (parabolic) via analytic continuation to imaginary times, so in that sense one could call it parabolic, but I'm not sure if Mathematicians have a reserved term to account for the fact that the solutions are complex numbers.
 

1. What is the Schrodinger equation?

The Schrodinger equation is a mathematical equation that describes how the wave function of a quantum system evolves over time.

2. What does the Schrodinger equation represent?

The Schrodinger equation represents the fundamental equation of quantum mechanics, which governs the behavior of particles at the microscopic level.

3. Is the Schrodinger equation a differential equation?

Yes, the Schrodinger equation is a partial differential equation that describes the time evolution of the wave function in terms of the system's energy and potential.

4. What kind of differential equation is the Schrodinger equation?

The Schrodinger equation is a second-order partial differential equation, as it involves the second derivative of the wave function with respect to both time and position.

5. Why is the Schrodinger equation important?

The Schrodinger equation is important because it is the foundation of quantum mechanics and has been successfully used to predict the behavior of particles at the atomic and subatomic level.

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