The Definition of Waves in Quantum Mechanics

In summary, a wave in quantum mechanics is a function on the configuration space with values in a vector space, and it can behave in various ways depending on the experimental situation. It is not the same as a wavefunction, which is an abstract number representing the probability of a system's state. There is also a concept of wave-particle duality, though there is debate over whether this term is accurate.
  • #1
snackster17
27
0
I hear the term Wave used in extreme frequencies whenever Quantum Mechanics is discussed but I am not entirely sure what exactly is a wave.
Can a wave be thought as a particle whose position is unspecified with multiple areas where it may impact the surface of another object.
Or is a wave a group of particles bundled up?
thanks.
 
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  • #2
A wave is a wave. It is a function on the configuration space (3n-dimensional for an n-particle system), not in the ordinary space. It has values in some vector space. For an electron with spin it will be 2 or 4 dimensional complex.

There are different kind of waves. Almost every parameter of a physical system can sometimes behave in a wavy way.

The "waves" in quantum theory of one particle determine the probabilities of the response of particle's detectors (you can try to detect position, momentum, energy, spin). Their generation and propagation depends on the whole experimental situation. The rest is in the math.
 
  • #3
Wave is collective behavior of particles that can not be explained by independent behavior of each particle separately.
 
  • #4
A wave in quantum mechanics is something that behaves like a wave.

Think 'oscillatory'.
 
  • #5
I just want to be clear, are we talking about "wave" or "wavefuntion"? The former is Granpa's reading, the latter is the probabilistic reading of Zonde (I think)
 
  • #6
Wave-particle duality may be a misnomer and Field-particle duality may be the right term.
 
  • #7
Reylan said:
Wave-particle duality may be a misnomer and Field-particle duality may be the right term.

Then again, it might not be.
 
  • #8
snackster17 said:
I hear the term Wave used in extreme frequencies whenever Quantum Mechanics is discussed but I am not entirely sure what exactly is a wave.
Can a wave be thought as a particle whose position is unspecified with multiple areas where it may impact the surface of another object.
Or is a wave a group of particles bundled up?
thanks.

The oscillating quantity in a quantum mechanics wavefunction (which is a wave) is an abstract number such that when it is squared, the new number is the probability that the system is in a particular state. A state may contain everything that is measurable about one or many particles including their locations, momenta, and energies.

Put another way, the oscillating quantity is the root of the probability of having a specific series of numbers describing a physical system, at time t (usually).
 
  • #9
nismaratwork said:
Then again, it might not be.
Yet another form of uncertainty?
 
  • #10
Reylan said:
Yet another form of uncertainty?

No, I was dismissing what you said in a sarcastic fashion, if I recall. This was nearly 2 weeks ago... but that's how I remember it.
 
  • #11
nismaratwork said:
No, I was dismissing what you said in a sarcastic fashion, if I recall. This was nearly 2 weeks ago... but that's how I remember it.

Your dismissal that necessitated sarcasm is well appreciated... but you could have done better without it.
 
  • #12
Reylan said:
Your dismissal that necessitated sarcasm is well appreciated... but you could have done better without it.

Perhaps... it was a 6 word post 2 weeks ago, it's not ringing a lot of bells for me.
 

1. What is the definition of a wave in quantum mechanics?

The definition of a wave in quantum mechanics is a disturbance or oscillation that travels through space and time, carrying energy but not matter. In quantum mechanics, waves are used to describe the behavior of subatomic particles, such as electrons, which exhibit both wave-like and particle-like properties.

2. How are waves described in quantum mechanics?

In quantum mechanics, waves are described by mathematical equations, specifically the Schrödinger equation. This equation allows us to calculate the probability of finding a particle at a certain location and time, based on its wave function. The wave function represents the probability amplitude of the particle at different points in space.

3. What is the wave-particle duality in quantum mechanics?

The wave-particle duality is a fundamental concept in quantum mechanics that states that all particles can exhibit both wave-like and particle-like behavior. This means that particles can behave like waves, with properties such as interference and diffraction, and also like particles, with properties such as mass and momentum.

4. How do waves in quantum mechanics differ from classical waves?

Waves in quantum mechanics differ from classical waves in several ways. Classical waves are continuous and can have any amplitude, whereas quantum waves are discrete and can only have certain discrete energy levels. Additionally, classical waves can be observed and measured at any point in space, whereas quantum waves can only be observed through interactions with other particles.

5. What is the uncertainty principle and how does it relate to waves in quantum mechanics?

The uncertainty principle, also known as Heisenberg's uncertainty principle, states that it is impossible to know the exact position and momentum of a particle simultaneously. This is because in quantum mechanics, the act of measuring one property of a particle can change its other properties. This principle applies to waves in quantum mechanics because the more precisely we know the position of a particle, the less we know about its momentum, and vice versa.

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