Why does the amplitude of a ripple tells us that it is a particle?

The quote below is from Matt Strassler’s blog: a particle is a ripple with many crests and troughs; its amplitude, relative to its overall length, is what tells you that it is a single particle. If I understand correctly, what he calls “ripple” is “probability wave”. Why is it that the amplitude of a probability … Read more

What do we mean by Unitary Dynamics in Quantum Computing?

In the afterword to the Tenth Anniversary Edition of the book Quantum Computation and Quantum Information the authors say: For many years, the conventional wisdom was that coherent superposition-preserving unitary dynamics was an essential part of the power of Quantum Computers. Since I am just starting reading this subject, so I am unable to understand … Read more

How can I make this toy quantum random walk model unitary?

Take a toy (1+1)-dimensional lattice model of the universe. A particle begins at x=0 at t=0. It has an amplitude 1/√2 to move one step to the left and amplitude 1/√2 to move one step to the right. At time t=1 it will either be at x=−1 or x=+1 with probability 12 each. At time … Read more

Propagators and Probabilities in the Heisenberg Picture

I’m trying to understand why |⟨0|ϕ(x)ϕ(y)|0⟩|2 is the probability for a particle created at y to propagate to x where ϕ is the Klein-Gordon field. What’s wrong with my reasoning below? We can write ϕ(x)=∫d3p(2π)3√2Ep(ape−ip.x+a†peip.x) Then acting with the position operator (which presumably we can write in terms of the a somehow) we find that … Read more

Proof of Liouville’s theorem: Relation between phase space volume and probability distribution function

I understand the proof of Liouville’s theorem to the point where we conclude that Hamiltonian flow in phase-space is volume preserving as we flow in the phase space. Meaning the total derivative of any initial volume element is 0. From here, how do we say that probability distribution function is constant as we flow in … Read more

Why does Hamiltonian follow the property H∗ij=HjiH^*_{ij} = H_{ji} ?

I was reading Feynman’s Lectures III’s Hamiltonian Matrix. There I found this property of Hamiltonian Matrix: The Hamiltonian has one property that can be deduced right away, namely, that H∗ij=HjiThis follows from the condition that the total probability that the system is in some state does not change. If you start with a particle—an object … Read more

E. T. Jaynes’ subjectivism vs measurement of distributions

In his paper, E. T. Jaynes argues that entropy is a measure of our ignorance about a system. As such, the probability distribution of states {pk} has to be chosen in the most unbiased way, thus maximizing the entropy constrained to all the available information. This is a subjectivist point of view because treats probabilities … Read more

Flipping a coin with same initial conditions

Today, in my physics class my teacher was talking about how we can never predict the outcome of a coin flip. So I thought: Will the outcome of a coin flip be the same if we do not change the initial conditions (such as launch angle, force position where force is applied,etc.)? Intuitively, I feel … Read more

Why quantum mechanics uses density operators instead of probability distributions over state space?

Whenever I try to get my head around mixed states I am referred to the notion of density operators. I think that density operators were introduced to represent mixed states as operators. For what I read I see that a mixed state is just a bunch of pure states where each state has assigned some … Read more

Is quantum mechanics truly probabilistic?

Probability arises inherently from a lack of information. For example, if I were to take a ball out of a bag with 3 yellow and 2 white balls, I would have a 0.6 probability of getting a yellow and a 0.4 probability of getting a white ball. However, these only apply because I cannot see … Read more