mfb said:You can find things that follow a normal distribution in QM, but I would not call this "relationship between QM and normal distribution" in the same way I don't see a "relationship between the normal distribution and the number 3".
mfb said:quantum mechanics is more than pure probability theory.
Simon Phoenix said:Then, assuming ideal measurements, the probability of getting spin up in a measurement of spin-z is 1, and the probability of getting spin down is 0. Not really very Gaussian :-)
Simon Phoenix said:Now suppose we measure spin-x, then the probability of getting a spin up result is now 1/2 and the probability of getting a spin down result is 1/2. A uniformly random distribution.
Simon Phoenix said:Let's take some more examples - if we have a coherent state of light and make a measurement of photon number - then we'll get a Poisson distribution (in many runs of the same experiments, of course). Measurement of the field quadrature operator of the same coherent state will give us a Gaussian (if I recall correctly). Take a photon number state of the EM field and measure it's phase - you'll get a uniformly random distribution.
Simon Phoenix said:Could you perhaps be a bit more specific because your question doesn't make a lot of sense to me.
Given ##\psi(x,t)##, you want ##|\psi(x,t)|^2## at fixed position ##x=x_0## to follow Gaussian profile with time, is that what you mean?forcefield said:I am thinking about whether it is possible to calculate QM probabilities by assuming that the measurement probability changes like normal distribution as time goes by.
forcefield said:You know there is this so called phase that you can throw away when you calculate probabilities in QM
forcefield said:I think that makes it Gaussian too just like throwing coins
Only phases in the basis where you want to calculate the probabilities, at the time when you want to calculate them.forcefield said:You know there is this so called phase that you can throw away when you calculate probabilities in QM.
No.forcefield said:I am thinking about whether it is possible to calculate QM probabilities by assuming that the measurement probability changes like normal distribution as time goes by.
No, I'm not considering wave functions. Actually I haven't studied them seriously yet.blue_leaf77 said:Given ##\psi(x,t)##, you want ##|\psi(x,t)|^2## at fixed position ##x=x_0## to follow Gaussian profile with time, is that what you mean?
Yes, I thought about that and it looks like a relative phase of pi/2 is required.Simon Phoenix said:You're talking here about a global phase factor - you certainly can't ignore the relative phases between terms in a superposition when calculating probabilities. Recall that to calculate a probability in QM we're taking the square modulus of sums of complex numbers.
The only entity which connects QM with probabilistic interpretation is the wavefunction.forcefield said:No, I'm not considering wave functions. Actually I haven't studied them seriously yet.
I think one should consider a period of π here.mfb said:The relative phase in a superposition can be everything (well, as it is a phase, it is usually restricted to the range from 0 to 2pi).
That does not make sense.forcefield said:I think one should consider a period of π here.
Yes, I was sloppy there. The length of the period doesn't really matter but if you look at the shape of normal distribution it is more like half-circle than full-circle.mfb said:That does not make sense.
Sorry, but that made even less sense.forcefield said:Yes, I was sloppy there. The length of the period doesn't really matter but if you look at the shape of normal distribution it is more like half-circle than full-circle.
QM probability, also known as quantum probability, is a mathematical concept used in quantum mechanics to describe the likelihood of a particular outcome or observation in a quantum system. It is based on the principles of superposition and uncertainty, and is often represented by a wave function.
QM probability differs from classical probability in that it allows for the possibility of multiple outcomes occurring simultaneously, rather than just one. It also takes into account the wave-like behavior of particles at the quantum level, which is not present in classical systems.
The normal distribution, also known as the Gaussian distribution, is a probability distribution that is commonly seen in natural phenomena. It is characterized by a bell-shaped curve, with the majority of data points falling near the mean and fewer points further away from the mean. The normal distribution is often used to model random variables in statistics and is an important concept in QM probability.
The normal distribution is a key tool in QM probability because it allows for the prediction of outcomes in quantum systems. This is because the wave function, which represents the probability of finding a particle at a specific location, can be described by a normal distribution. This allows scientists to make predictions about the likelihood of a particle being in a certain location or having a certain energy level.
No, the normal distribution is not applicable to all quantum systems. It is most commonly used in systems that exhibit wave-like behavior, such as photons and electrons. Other quantum systems, such as those involving spin states, may require different mathematical models to describe their probabilities. It is important for scientists to carefully consider the specific characteristics of a quantum system when using the normal distribution to make predictions.