Comparison of quantum and classical equations

In summary, the conversation discusses the information needed to define a well-defined problem in the context of a particle in a potential. It is mentioned that since the equations of motion are second order with respect to time derivatives, the initial position and velocity of the particle must be known. In the quantum case, it is suggested that only the initial wavefunction needs to be known, which may require less information. The conversation also touches on the question of whether two numbers or a whole function require more information to specify, as well as the need for boundary conditions in the quantum case.
  • #1
sachi
75
1
Hi, we have a particle in a potential. We are asked to state what information we need to have a well defined problem, and since the equations of motion are second order wrt time derivates we need to know the position of the particle initially and its velocity. We are then asked "in the quantum physics of one particle in a potential how much initial information do you have to give to have a well defined problem? Do we have to specify less or more in the quantum case?" I think in the quantum case we just need to know the the initial wavefunction. Does this mean we need to know less?

Thanks
 
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  • #2
Which takes more information to specify, two numbers or a whole function?
 
  • #3
Also bounday conditions are needed in the quantum case.

Daniel.
 

1. What is the main difference between quantum and classical equations?

The main difference between quantum and classical equations is that quantum equations describe the behavior of particles at a microscopic level, while classical equations describe the behavior of macroscopic objects. Quantum equations take into account the probabilistic nature of particles and their wave-like properties, while classical equations treat particles as definite, measurable objects.

2. How do quantum equations and classical equations relate to each other?

Quantum equations and classical equations are closely related, with classical equations often being seen as a simplified version of quantum equations. In certain scenarios, such as at large scales or low energies, quantum equations can be approximated by classical equations. However, in other scenarios, such as at a subatomic level, classical equations are not accurate and must be replaced with quantum equations.

3. Which equations are used in everyday life, quantum or classical?

Classical equations are used in everyday life because they accurately describe the behavior of macroscopic objects. For example, classical mechanics is used to understand the movement of cars, airplanes, and other large objects. However, quantum equations are used in many modern technologies, such as transistors in computers and lasers in medical equipment, showing the importance and relevance of both types of equations.

4. Can quantum equations be used to predict the behavior of particles?

Quantum equations can be used to predict the behavior of particles, but they do so in a probabilistic manner. Unlike classical equations, which give definite outcomes, quantum equations can only predict the probability of a certain outcome. This is due to the inherent uncertainty and randomness of particles at a quantum level.

5. What are some real-world applications of quantum equations?

Quantum equations have a wide range of real-world applications, including in the fields of quantum computing, quantum cryptography, and quantum communication. They are also used in medical imaging technology, such as MRI machines, and in studying the behavior of atoms and molecules in chemistry and biology. Additionally, they play a crucial role in understanding and developing new materials and technologies, such as superconductors and nanotechnology.

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