Schrödinger equation: macro level

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SUMMARY

The Schrödinger equation (SE) can theoretically describe macroscopic objects, including their location, as there is no inherent scale limitation within the equation. However, the complexity of the Hamiltonian required for accurate modeling of macroscopic systems poses significant challenges. Practitioners often prefer the Heisenberg picture for modeling simple macroscopic objects, such as superconducting devices, due to its advantages in handling dissipation. Notably, solid-state qubits, which can be several square microns in size, can be effectively described using solvable forms of the Schrödinger equation.

PREREQUISITES
  • Understanding of the Schrödinger equation
  • Familiarity with Hamiltonian mechanics
  • Knowledge of quantum mechanics principles
  • Experience with solid-state physics concepts
NEXT STEPS
  • Research Hamiltonian formulations for macroscopic systems
  • Explore the Heisenberg picture in quantum mechanics
  • Study the application of the Schrödinger equation to solid-state qubits
  • Investigate the role of dissipation in quantum systems
USEFUL FOR

Physicists, quantum mechanics researchers, and engineers working with superconducting devices or solid-state qubits will benefit from this discussion.

_Andreas
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Is it possible, in theory, to describe a macroscopic object with the Schrödinger equation (its location for example)?
 
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Yes, there is no "scale" in the SE. The main problem is that you of course also need an relevant Hamiltonian for what you are modeling; preferably one that can be used to solve the problem and for most macroscopic objekt the Hamiltonian is very complicated.

In reality, most people tend to prefer the Heisenberg (or more generally interaction) picture when they model 'simple' macroscopic objects such as superconducting devices for various technical reasons (mainly because it is easier to handle dissipation) but you can always re-write this as a SE

Also, note that solid state qubits are quite large, several square microns (which doesn't sound like much, but you can e.g. easily see them in a decent optical microscope). and they are quite well described by 'simple' SE that can actually be solved.
 
Thanks! In another discussion I'm involved in I stated rather confidently that it is indeed possible, but then it suddenly struck me that my memory might be at fault.
 

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