Need some help with wave function/QM properties. Thanks

In summary, a wave function or wavefunction is a complex function in quantum mechanics that describes the probability amplitude of a particle's quantum state and its behavior. It is used to determine the probability of finding a particle in a certain position at a certain time. In simpler terms, it is a way to measure the likelihood of a particle being in a specific area. The wavefunction is normalized, meaning that when integrated over all space, it equals 1. It is not directly related to the wave created by a vibrating molecule, but can be used to calculate the probability of the molecule's position. Overall, the wavefunction is a key concept in quantum mechanics for understanding the behavior of particles.
  • #1
nukeman
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Can someone explain the following statement for me? The best you can, would really appreciate it.

"A wave function or wavefunction is a probability amplitude in quantum mechanics describing the quantum state of a particle and how it behaves. "

I am trying to learn/understand how something like a molecule vibrates, and how this vibration creates a wave function that can affect other particles, or other things.
 
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  • #2
A wavefunction psi(x,t) is some complex function of space and time. If you take the absolute square of it |ps(x,t)|^2 then you get roughly the probability distribution that the particle is in position between x and x+dx, at time t.
 
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  • #3
In the simpliest terms possible, can you expand the following statement?

"A wave function or wavefunction is a probability amplitude in quantum mechanics describing the quantum state of a particle and how it behaves."
 
  • #4
nukeman said:
I am trying to learn/understand how something like a molecule vibrates, and how this vibration creates a wave function that can affect other particles, or other things.
That will prove difficult since a wave from a vibrating molecule has nothing to do with the wavefunction. It may create compression waves in a material, but that is completely different.

nukeman said:
In the simpliest terms possible, can you expand the following statement?
Do you know what a probability distribution is? In QM there is a function that is a complex function (as in [itex]i[/itex]) called a wavefunction. If you want to know the probability that a particle will be found in a certain area, you integrate the absolute square of the wavefunction over the area in question. The absolute square of the wavefunction is the complex conjugate of the function times the function.

The wavefunction is normalized which means that if you integrate over all space it equals 1 (which just means that the particle will be found somewhere if you can look everywhere).
 
  • #5
Not too sure on probability distribution. Is it mainly the statistical probability of something like a particle, being some where we are looking at?

So you are saying that Quantum mechanical waves would have nothing to do with a vibrating molecule?

Is there anything quantum mechanical about a vibrating molecule?
 

1. What is a wave function in quantum mechanics?

A wave function is a mathematical representation of a particle's quantum state. It describes the probability of finding the particle at a certain position and time, and contains all the information about the particle's properties and behavior.

2. How is a wave function determined?

A wave function is determined by solving the Schrödinger equation, which is a fundamental equation in quantum mechanics. This equation takes into account the potential energy of the system and the mass of the particle, and allows us to calculate the wave function at any given time and position.

3. What are the properties of a wave function?

A wave function has several important properties, including being continuous, single-valued, and square-integrable. It also must satisfy certain boundary conditions and must be normalized, meaning that the sum of all its possible values must equal 1.

4. How does a wave function relate to the uncertainty principle?

The wave function is closely related to the uncertainty principle, which states that it is impossible to know both the position and momentum of a particle with absolute certainty. The wave function describes the probability of finding a particle at a certain position, and as the position becomes more certain, the momentum becomes more uncertain and vice versa.

5. What is the role of the wave function in quantum mechanics?

The wave function is a fundamental concept in quantum mechanics and plays a crucial role in understanding the behavior of particles at the quantum level. It allows us to make predictions about the behavior of particles and is used in many calculations and experiments in the field of quantum mechanics.

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