Finding probability of changing states

In summary, the conversation discusses the derivation of an expression that represents the probability of being in a different state from the initial state in adiabatic passage. The first term in the expression is 1 by unitarity, while the last term represents the probability of remaining in the initial state. The difference between these two terms gives the total probability of not being in the initial state.
  • #1
TheCanadian
367
13
I am following the derivation shown in this link on adiabatic passage.

I have posted one part below:

Screen Shot 2016-07-15 at 11.53.04 AM.png


I am simply wondering how this expression was derived and how it indicates the probability of being in a state that is different from the initial state? How exactly is this represented by:

$$ \langle \hat{U}^\dagger(t_1,t_0)\hat{U}(t_1,t_0)\rangle - \langle \hat{U}^\dagger(t_1,t_0)\rangle\langle \hat{U}(t_1,t_0)\rangle $$
 
Physics news on Phys.org
  • #2
The last term in your last expression is the probability that you will remain in the initial state. The first term is 1 by unitarity. The difference of these terms is the total probability of not being in the initial state.
 
  • Like
Likes Jilang and TheCanadian

What is the definition of probability in relation to changing states?

Probability in relation to changing states refers to the likelihood or chance of a particular event or outcome occurring when there is a change in a system or state. It is a measure of the uncertainty or randomness associated with the change.

How is probability of changing states calculated?

The probability of changing states is calculated by dividing the number of desired outcomes by the total number of possible outcomes. This can be expressed as a decimal, fraction, or percentage.

What factors can influence the probability of changing states?

Several factors can influence the probability of changing states, including the initial state of the system, the nature of the change, and any external influences or variables that may affect the outcome. Other factors such as randomness or uncertainty can also play a role.

Can probability of changing states be predicted?

While probability itself is a predictable measure, the exact outcome of a change in states cannot always be predicted with certainty. This is due to the influence of various factors and the inherent randomness in certain systems.

How is probability of changing states used in scientific research?

Probability of changing states is a crucial concept in scientific research, particularly in fields such as physics, chemistry, and biology. It is used to model and analyze various phenomena, make predictions and decisions, and understand the behavior of complex systems. It also helps scientists determine the reliability and validity of their findings.

Similar threads

A Asymptotic states in the Heisenberg and Schrödinger pictures
    • Quantum Physics
Replies
8
Views
1K
A Heisenberg picture and Path integrals (Zee QFT)
    • Quantum Physics
Replies
15
Views
2K
A Changing Hamiltonian with some eigenvalues constant
    • Quantum Physics
Replies
5
Views
910
I Realizing a Quantum Mechanical Watch-Stop
    • Quantum Physics
Replies
4
Views
773
A Matrix representation of a unitary operator, change of basis
    • Quantum Physics
Replies
1
Views
960
I How to solve 2nd order TDSE for a Gaussian-kicked harmonic oscillator?
    • Quantum Physics
Replies
6
Views
1K
I Physical interpretation of this coherent state
    • Quantum Physics
Replies
3
Views
932
I Feynman's Lectures volume III (Ch:8) -- Resolution of vector states
    • Quantum Physics
Replies
4
Views
783
A Thought experiment in relativistic quantum mechanics?
    • Quantum Physics
Replies
4
Views
804
A Quantitative description of successive Stern-Gerlach measurements
    • Quantum Physics
Replies
1
Views
525

Hot Threads

Recent Insights

Back
Top