Tutorial 9 - UBC Physics
... polarizations, we can show that the average probability of passing though the first polarizer is t/2 (can you prove this?). ln parts c and e, you have calculated the probability for a photon that has passed through the first polarizer to pass through the second polarizer, and the probability for a p ...
... polarizations, we can show that the average probability of passing though the first polarizer is t/2 (can you prove this?). ln parts c and e, you have calculated the probability for a photon that has passed through the first polarizer to pass through the second polarizer, and the probability for a p ...
Theory of quantum state control with solid-state qubits Research supervisor
... vast. Essential for these developments, however, is the ability to take a quantum system with a few discrete states, such as an exciton in a quantum dot or impurity state in a crystal, and control its wavefunction – i.e., prepare it in a specified state. Such an ability would also provide new probes ...
... vast. Essential for these developments, however, is the ability to take a quantum system with a few discrete states, such as an exciton in a quantum dot or impurity state in a crystal, and control its wavefunction – i.e., prepare it in a specified state. Such an ability would also provide new probes ...
Quantum Notes (Chapter 16)(Powerpoint document)
... For each value of n (1, 2, 3 etc.) there are n2 different wave functions, any of which are valid for an electron of the H atom. First of all, what is a wavefunction? It is a mathematical description of the wave properties of an electron in the H atom. As a wavefunction, it has the properties of a wa ...
... For each value of n (1, 2, 3 etc.) there are n2 different wave functions, any of which are valid for an electron of the H atom. First of all, what is a wavefunction? It is a mathematical description of the wave properties of an electron in the H atom. As a wavefunction, it has the properties of a wa ...
Probability of Events
... The Addition Rule When events are not mutually exclusive, the addition rule is given by: p(A or B) = p(A) + p(B) - p(A and B) p(A and B) is the probability that both event A and event B occur simultaneously This formula can always be used as the addition rule because p(A and B) equals zero when the ...
... The Addition Rule When events are not mutually exclusive, the addition rule is given by: p(A or B) = p(A) + p(B) - p(A and B) p(A and B) is the probability that both event A and event B occur simultaneously This formula can always be used as the addition rule because p(A and B) equals zero when the ...
AAAI Proceedings Template
... we postulate a set of (2m+1) states of confidence about the presence or absence of the target: { |m, |m+1 , …, |1, |0, |+1, …, |+m1, |+m }. The state |j can be interpreted as a (2m+1) column vector with zeros everywhere, except that it has 1.0 located at the row corresponding to index j. ...
... we postulate a set of (2m+1) states of confidence about the presence or absence of the target: { |m, |m+1 , …, |1, |0, |+1, …, |+m1, |+m }. The state |j can be interpreted as a (2m+1) column vector with zeros everywhere, except that it has 1.0 located at the row corresponding to index j. ...
1. You are given one of two quantum states of a single qubit: either
... |vv⊥ i − |v⊥ vi = (α|0i + β |1i) ⊗ (−β̄ |0i + ᾱ|1i) − (−β̄ |0i + ᾱ|1i) ⊗ (α|0i + β |1i) = (−α β̄ + β̄ α)|00i + (|α|2 + |β |2 )|01i − (|β |2 + |α|2 )|10i + (β ᾱ − ᾱβ )|11i = |01i − |10i , where in the last equality we used the normalization condition. Hence, |Ψ− i is rotationally invariant; for a ...
... |vv⊥ i − |v⊥ vi = (α|0i + β |1i) ⊗ (−β̄ |0i + ᾱ|1i) − (−β̄ |0i + ᾱ|1i) ⊗ (α|0i + β |1i) = (−α β̄ + β̄ α)|00i + (|α|2 + |β |2 )|01i − (|β |2 + |α|2 )|10i + (β ᾱ − ᾱβ )|11i = |01i − |10i , where in the last equality we used the normalization condition. Hence, |Ψ− i is rotationally invariant; for a ...
6. Quantum Mechanics II
... Consider a particle of energy E approaching a potential barrier of height V0, and the potential everywhere else is zero and E > V0. In all regions, the solutions are sine waves. In regions I and III, the values of k are: ...
... Consider a particle of energy E approaching a potential barrier of height V0, and the potential everywhere else is zero and E > V0. In all regions, the solutions are sine waves. In regions I and III, the values of k are: ...
hydrogen
... The probability of finding the electron does not depend upon the azimuthal angle since (11) *ml ( )ml ( ) eiml eiml 1 The three dimensional behavior of the probability density is completely dependent on the product of the radial probability density Pnl ( r ) Rnl* ( r ) Rnl ( r ) and a ...
... The probability of finding the electron does not depend upon the azimuthal angle since (11) *ml ( )ml ( ) eiml eiml 1 The three dimensional behavior of the probability density is completely dependent on the product of the radial probability density Pnl ( r ) Rnl* ( r ) Rnl ( r ) and a ...
1 Heisenberg Uncertainty Principle
... δp ∼ h/λ. The net result is that the product (δx)(δp) should be of order Planck’s constant, or (δx)(δp) ∼ h. (We are not following factors of 2 or π at this point.) A question that has been studied ever since Heisenberg’s original paper is whether a precise inequality can be established for the cas ...
... δp ∼ h/λ. The net result is that the product (δx)(δp) should be of order Planck’s constant, or (δx)(δp) ∼ h. (We are not following factors of 2 or π at this point.) A question that has been studied ever since Heisenberg’s original paper is whether a precise inequality can be established for the cas ...
Lecture 1
... separate columns. In columns 1 and 2 we keep a count of electrons reaching the detector attended by a flash near hole 1 and hole 2, respectively. In column 3 we record those electrons which reached the detector without producing a flash. The data in columns 1 and 2 give rise to the probability distr ...
... separate columns. In columns 1 and 2 we keep a count of electrons reaching the detector attended by a flash near hole 1 and hole 2, respectively. In column 3 we record those electrons which reached the detector without producing a flash. The data in columns 1 and 2 give rise to the probability distr ...
Another version - Scott Aaronson
... A Few Other Things I’ve Worked On The limitations of quantum computers (e.g., for finding collisions in hash functions); the possibility of quantum-secure cryptography What’s the largest possible quantum speedup? (The Forrelation and k-fold Forrelation problems) Quantum computing and the black-hole ...
... A Few Other Things I’ve Worked On The limitations of quantum computers (e.g., for finding collisions in hash functions); the possibility of quantum-secure cryptography What’s the largest possible quantum speedup? (The Forrelation and k-fold Forrelation problems) Quantum computing and the black-hole ...
CHAPTER 9: Statistical Physics
... However, we are only interested in the molecule, not the container. For example, what is the probability for the molecule to have (x,v)? count # of accessible states for the system for given (x,v) of the ...
... However, we are only interested in the molecule, not the container. For example, what is the probability for the molecule to have (x,v)? count # of accessible states for the system for given (x,v) of the ...
Vargas
... now the sum formally includes any 4-dimensional compact orbifold O with metric g, and the Euclidean orbifold action is given by I (O, g ) 1 ( R 2)d ( g ) 1 Kd (h) 16G O 8G S -the induced metric and the curvature will have singularities at the fixed points of the orbifolds. -as observe ...
... now the sum formally includes any 4-dimensional compact orbifold O with metric g, and the Euclidean orbifold action is given by I (O, g ) 1 ( R 2)d ( g ) 1 Kd (h) 16G O 8G S -the induced metric and the curvature will have singularities at the fixed points of the orbifolds. -as observe ...
Probability amplitude
In quantum mechanics, a probability amplitude is a complex number used in describing the behaviour of systems. The modulus squared of this quantity represents a probability or probability density.Probability amplitudes provide a relationship between the wave function (or, more generally, of a quantum state vector) of a system and the results of observations of that system, a link first proposed by Max Born. Interpretation of values of a wave function as the probability amplitude is a pillar of the Copenhagen interpretation of quantum mechanics. In fact, the properties of the space of wave functions were being used to make physical predictions (such as emissions from atoms being at certain discrete energies) before any physical interpretation of a particular function was offered. Born was awarded half of the 1954 Nobel Prize in Physics for this understanding (see #References), and the probability thus calculated is sometimes called the ""Born probability"". These probabilistic concepts, namely the probability density and quantum measurements, were vigorously contested at the time by the original physicists working on the theory, such as Schrödinger and Einstein. It is the source of the mysterious consequences and philosophical difficulties in the interpretations of quantum mechanics—topics that continue to be debated even today.