Schrödinger equation: macro level

In summary, it is possible in theory to describe a macroscopic object with the Schrödinger equation, as there is no "scale" in the SE. However, the main problem is finding a relevant Hamiltonian for the object being modeled. Most people prefer the Heisenberg or interaction picture for modeling "simple" macroscopic objects, but this can always be rewritten as a SE. Solid state qubits, which can be seen with an optical microscope, are well described by simple SE equations that can be solved.
  • #1
_Andreas
144
1
Is it possible, in theory, to describe a macroscopic object with the Schrödinger equation (its location for example)?
 
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  • #2
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.
 
  • #3
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.
 

FAQ: Schrödinger equation: macro level

1. What is the Schrödinger equation at the macro level?

The Schrödinger equation at the macro level is a mathematical equation that describes the behavior of particles and systems at the scale of everyday objects. It combines classical mechanics and quantum mechanics to predict the position and momentum of macroscopic objects.

2. How does the Schrödinger equation apply to macroscopic objects?

At the macro level, the Schrödinger equation is used to describe the behavior of particles and systems in terms of their wave functions. These wave functions represent the probability of finding a particle in a particular state, and can be used to predict the overall behavior of macroscopic objects.

3. Can the Schrödinger equation accurately predict the behavior of macroscopic objects?

While the Schrödinger equation has been successful in predicting the behavior of microscopic particles, it is not as accurate at the macro level. This is due to the fact that macroscopic objects are subject to many more variables and interactions than individual particles, making it difficult to accurately predict their behavior.

4. What are some limitations of the Schrödinger equation at the macro level?

One limitation of the Schrödinger equation at the macro level is that it does not take into account the effects of gravity. This is because the equation was developed for non-relativistic systems, and does not include the principles of general relativity. In addition, the equation also does not account for the uncertainty and unpredictability of macroscopic objects.

5. How is the Schrödinger equation used in practical applications at the macro level?

Despite its limitations, the Schrödinger equation at the macro level is still used in practical applications, such as in the development of new materials and technologies. It is also used in fields like chemistry and biology, where it can help predict the behavior of larger molecules and complex systems. Additionally, the principles of the Schrödinger equation have also been applied to fields such as economics and social sciences.

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