Classical and quantum mechanics

In summary, classical mechanics and quantum mechanics differ in their approach to understanding the behavior of matter. Classical mechanics focuses on macroscopic quantities and uses the concept of a trajectory to describe the motion of particles. On the other hand, quantum mechanics deals with subatomic scales and relies on the concept of probabilities to describe the behavior of particles. Additionally, quantum mechanics views matter as having a wave-like nature, while classical mechanics treats particles as discrete entities. While classical mechanics can be used to solve problems on a macroscopic scale, quantum mechanics provides a more detailed and accurate understanding of the behavior of matter.
  • #1
shankar
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can anyone tell me the difference between classical mechanics and quantum mechanics??
 
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  • #2
Originally posted by shankar
can anyone tell me the difference between classical mechanics and quantum mechanics??


Roughly - Classical mechanics deals with quantities on a macroscopic scale and quantum mechanics deals with quantities on a sub atomic scale.

Classical mechanics use the idea that a particle is at a particular place at a given time and thus uses the concept of a trajectory. Quantum mechanics deals only with probabilities of where a partilce will be found, the momentum and energy it will have etc.

Pete
 
  • #3
Quantum mechanics is the more detailed and more correct accounting of the "what and why" of matter. All classical problems can be solved using quantum rules, but when your dealing with large numbers of particles, the "probabilities" of quantum mechanics start to appear to be more absolute.

For example, in quantum mechanics, you would be interested in what happens to a single neutron. Depending on the condition, there are various probabilities to the outcomes (80% likely to do this, 20% likely to do that).

When you have billions of billions of billions of particles, the most probable things seem dominant and the least probable things go unnoticed {WARNING: QUANTUM OVERSIMPLIFICATION} Who cares if a few of your electrons suddenly "tunnel" into the next galaxy. THere goes one right now! But you're fine, because most of the rest did what we expected them to do.
 
  • #4
Quantum mechanics deals with things very differently to classical mechanics. Quantum is all about waves, the dynamics of all things is determined by waves. Classical things like momentum and position don't have the same meaning, they are just borrowed terms. A typical example is spin, this is an intrinsic property of particles, but it doesn't mean the particle actualy spins. However, for waves with short wavelength, things get classical. Its like rays in optics. You can think about how a magnifying glass works just with a simple ray picture, you don't need to worry about interference of the light due to its wave nature. You can't explane diffraction in the same way.
 
  • #5
Quantum is all about waves, the dynamics of all things is determined by waves.
Er... no. A key conclusion of QM is that waves and particles are just different sides of the same coin. Mathematically, Schrodinger wave equations are ultimately equivalent to quantum particle equations. The schrodinger equation gets most limelight because it is generally considered as easier, and making more sense.
 
  • #6
Actualy there are sugestions on how to measure wave functions experimentaly. Mathematicaly you done need them its true. And I don't think there are any final conclusions about waves and particles.
 
  • #7
These questions always risk a confusion between the quantum amplitude wave - the thing that is supposed to collapse - and the wave nature of the particle. The particle's wave nature is a real thing that exists in spacetime and has physical things - like diffraction - happen to it. The amplitude "wave" is a thing expressed in complex numbers, that cannot be a thing in spacetime, and exists primarily in an abstract Hilbert Space. Operators act on it and produce "eigenvalues" and these eigenvalues generate the probabilities that something will happen in spacetime.

It is possible to imagine the amplitude is just a mathematical construct, part of a calculating algorithm. But the wave nature is experimentlly visible.
 

1. What is the difference between classical and quantum mechanics?

Classical mechanics is a theory that describes the motion of macroscopic objects in the world we experience, while quantum mechanics is a theory that describes the behavior of particles at the atomic and subatomic level.

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

Quantum mechanics is considered to be the more fundamental theory, as all classical mechanics principles can be derived from it. However, classical mechanics is still a useful and accurate theory for describing the behavior of macroscopic objects.

3. What is the uncertainty principle in quantum mechanics?

The uncertainty principle states that it is impossible to know both the exact position and momentum of a particle at the same time. This is due to the probabilistic nature of quantum mechanics, where the location of a particle can only be described in terms of a probability distribution.

4. How does quantum mechanics explain the behavior of particles?

Quantum mechanics describes particles as having wave-like properties, such as being able to exist in multiple states simultaneously. This allows for phenomena such as superposition and entanglement, which have no classical counterpart.

5. What is the role of mathematics in classical and quantum mechanics?

Mathematics is essential in both classical and quantum mechanics. Classical mechanics uses mathematical equations to describe the motion of objects, while quantum mechanics relies heavily on mathematical concepts such as wave functions and operators to describe the behavior of particles.

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