Probability amplitudes Definition and 22 Threads

I have one tremendous doubt about it. On ##t=0## the state of the oscillator is ##| \Psi (t) \rangle = | 1 \rangle ##. The perturbation is ##V(x)=\alpha x^3 = \alpha (\frac{\hbar}{2m\omega})^{3/2} (a+a^{\dagger})^3 = \gamma (a^3+3Na+3Na^{\dagger} + 3a + (a^{\dagger})^3)##. The only possible...

a and b were fairly easy to solve; but the c part which actually demands the probability! How are we suppose to fetch the value if the function can't even be normalized; I tried to make some assumptions like making the system bounded; but I don't think that it's the right way to do so... What...

If I want to get the spin angular momentum of a particle using the Stem-Gerlach experiment, I think I will find the spin 1/2 particle either spin up or spin down, but not both. I however want to ask this : Is there a non-zero probability that a particle which is spin-up in the z direction to be...

If I consider the MWI, one of the notions for what happens during measurement is that the initial wavefunction, if I use Dirac notation and two dimensions, ##|A\rangle+|B\rangle## undergoes the transformation ##(|A\rangle+|B\rangle)|E_{before}\rangle \rightarrow...

I am not sure what I can do with the equation. I realize that ## \vert c_1 \vert ^2 = \vert c_2 \vert ^2 = \frac{1}{2} ## does not mean that ## c_1 ^2 = c_2 ^2 = \frac{1}{2} ## or that ## c_1 = c_2 ##, so I don't know how to use it. I think ideally I might have something like ##P = \vert c_1...

Should I treat ψ1 as ψ and ψ 2 as ψ*?

Hi All, I would like to know who was the first scientist to use probability amplitudes in solving either math or physics problems. Best wishes, DaTario

Hi all, I am rather confused about the following concept. Assistance is greatly appreciated! A time-dependent probability amplitude can be written as $$\langle a_k| e^{-\frac{i}{\hbar}\hat{H}t} |\psi\rangle$$ where ##a_k## is an eigenvalue. Suppose I want the x-representation of the ket, I can...

Given two probability amplitude wavefunctions, one in position space ##\psi(r,k)## and one in wavenumber space ##\phi(r,k)##, where ##r## and ##k## are Fourier conjugates, how is it possible for the modulus squared, i.e., probability density, of BOTH wavefunctions to be normalized? It seems...

1. Given a Markov state density function: ## P((\textbf{r}_{n}| \textbf{r}_{n-1})) ## ##P## describes the probability of transitioning from a state at ## \textbf{r}_{n-1}## to a state at ##\textbf{r}_{n} ##. If ## \textbf{r}_{n-1} = \textbf{r}_{n}##, then ##P## describes the probability of...

Homework Statement I post here to check if I am in the right way to understand this point in the book. The wave function of free particle is ##Ae^{\frac{i}{\hbar}(px-Et)}##.This could be regarded as ##{\phi}(x,t)=Ae^{\frac{i}{\hbar}S(x,t)}##. ##S(x,t)## is the free particle's least action...

Hi, I am a student in the Netherlands, and I'll be attending university next year. However, I am doing some form of research on Quantum Computing with another student for our so-called "profielwerkstuk" but my understanding of Quantum Physics and math is sometimes not at the level that is...

Hi All, Was there any use of the concept of amplitudes of probability before their use in quantum mechanics? In connection to this question, who invented or was the first to use this resource? Best wishes, DaTario

So this is basic question but the more I read the more I am confusing myself! I was assuming that the wavelength of a photon was the same wavelength as the associated probability amplitude (although a complex number). So to make constructive interference it means one path takes say ten...

Given an electromagnetic field by its components E and B. How is this related to probability amplitudes of a Schrödinger wave function for the same field. Trying the same or at least a similar question from a different angle: given the E and B field, can we derive from it, in principle, not...

Im new to quantum mechanics and prof. James Binney writes the probability amplitude of going through two paths s and t, is the mod square of A(s)+A(t). Then he writes this as The mod square of A(s)+ mod square of A(t) + A(s)A(t)* + A(t)A(s). Why is it expanded like this? Could someone please...

When one says the probability amplitude for a quantity when it has probability P, which one does one take, the a+bi or the a-bi?

Suppose a Fock state contains 2 photons, both in the same spacetime mode and having the save (vertical) polarization. So we can write this state as |2>, or, if we want to emphacize its vertical polarization, we may write |2v> or |2v,0h>. Suppose now we want to measure polarization in the...

What's wrong with the following: \frac {d \left< E_{k} | \Psi \right>}{dt} = \frac{\partial \left< E_{k} \right|}{\partial t} \left| \Psi \right> + \left< E_{k} \right| \frac{\partial \left| \Psi \right>}{\partial t} = \frac{i}{\hbar} \left< E_{k} | H | \Psi \right> - \frac{i}{\hbar} \left<...

Homework Statement What physical phenomenon requires us to work with probability amplitudes rather than just with probabilities, as in other fields of endeavour? Homework Equations The Attempt at a Solution Not sure. The wording of the q throws me... phenomenon i.e...

What is the relationship between the "matter waves" described by de Broglie, the probability amplitude function and Schrödinger's wave equation? I've read the following: "The wavelengths postulated by de Broglie to be associated with the motions of particles are in reality the wavelengths...

I have this problem: The total number of waves Nw in a box is somewhat uncertain beause of the way the amplitude falls off. For a region of size DeltaX, call the uncertainty in the number of waves DeltaNw. a.) Relate DeltaNw to the uncertainty principle in the wavelength Delta(lambda)...