Indirect measurement
... we can do with a projective measurement is use P̂0 = |ψihψ|, P̂1 = Iˆ − P̂0 . In this case, if we get result 1 we know that the system cannot have been in state ψ , since hψ|P̂1 |ψi = 0. So it must have been in state φ. In the case of result 0, however, we cannot tell. We can design a similar projec ...
... we can do with a projective measurement is use P̂0 = |ψihψ|, P̂1 = Iˆ − P̂0 . In this case, if we get result 1 we know that the system cannot have been in state ψ , since hψ|P̂1 |ψi = 0. So it must have been in state φ. In the case of result 0, however, we cannot tell. We can design a similar projec ...
Quantum transport equations for Bose systems taking into account
... The problems of building a kinetic equation for Bose systems based on the microscopic approach were considered by Akhiezer and Peletminsky [21] and by Kirkpatrick and Dorfman [22–24]. The results of [22, 23] were extended and used to describe the trapped weakly-interacting Bose gases at finite temper ...
... The problems of building a kinetic equation for Bose systems based on the microscopic approach were considered by Akhiezer and Peletminsky [21] and by Kirkpatrick and Dorfman [22–24]. The results of [22, 23] were extended and used to describe the trapped weakly-interacting Bose gases at finite temper ...
Morse potential derived from first principles
... in polar coordinates for ω = 1, and considering atomic units, ~ = m = 1. In fact, it is this relationship that allows one to solve the QMO using ladder operators [29], and study this problem through supersymmetry [30]. As a consequence, our approach also provides a conceptual basis for the map betwe ...
... in polar coordinates for ω = 1, and considering atomic units, ~ = m = 1. In fact, it is this relationship that allows one to solve the QMO using ladder operators [29], and study this problem through supersymmetry [30]. As a consequence, our approach also provides a conceptual basis for the map betwe ...
The Fourier grid Hamiltonian method for bound state eigenvalues and eigenfunctions c.
... We consider a single particle of mass m moving in one linear dimension under the influence of a potential V. The nonrelativistic Hamiltonian operator K may be written as a sum of a kinetic energy and a potential energy operator A ...
... We consider a single particle of mass m moving in one linear dimension under the influence of a potential V. The nonrelativistic Hamiltonian operator K may be written as a sum of a kinetic energy and a potential energy operator A ...
Symmetry and statistics
... symmetry operation under consideration. However, this is not the only way a symmetry can be realized. It is possible that the physical laws and the Hamiltonian are invariant but the ground state is not. In the example of the left–right symmetry of the human body, an exact symmetry may be realized in ...
... symmetry operation under consideration. However, this is not the only way a symmetry can be realized. It is possible that the physical laws and the Hamiltonian are invariant but the ground state is not. In the example of the left–right symmetry of the human body, an exact symmetry may be realized in ...
M05/11
... As an example, we return to the case of spin-1/2. With the notation previously established, we have Aη (F (x)) = Aη ( 12 (1 + 3b·x)) = T (b). But F (x) = 12 (1 + 3b · x) is not a fuzzy set function. In fact −1 ≤ F (x) ≤ 2. There are other forms of F that will also give T (b), but they are worse in t ...
... As an example, we return to the case of spin-1/2. With the notation previously established, we have Aη (F (x)) = Aη ( 12 (1 + 3b·x)) = T (b). But F (x) = 12 (1 + 3b · x) is not a fuzzy set function. In fact −1 ≤ F (x) ≤ 2. There are other forms of F that will also give T (b), but they are worse in t ...
The pseudodifferential operator square root of the Klein
... parametric for a differential operator, that is, an inverse of the differential operator up to C” functions. For applications in physics and treating the subject by an intrinsic calculus see Fulling and Kennedy.’ In addition, PseudodifFerential operators can also be used to formulate generalizations ...
... parametric for a differential operator, that is, an inverse of the differential operator up to C” functions. For applications in physics and treating the subject by an intrinsic calculus see Fulling and Kennedy.’ In addition, PseudodifFerential operators can also be used to formulate generalizations ...
Path Integrals
... where m0 = dm/dq, etc. (This shows that a position-dependent mass for a particle gives rise to a frictional force.) If you have difficulty with this problem, you may want to review the classical variational principle. We can use the path integral to give an expression for the ground state wavefuncti ...
... where m0 = dm/dq, etc. (This shows that a position-dependent mass for a particle gives rise to a frictional force.) If you have difficulty with this problem, you may want to review the classical variational principle. We can use the path integral to give an expression for the ground state wavefuncti ...
Almost all pure quantum states are almost maximally entangled
... The 2-norm is the best suited norm for many computations. One example making use of the 2-norm has already been mentioned. Eq. (1) contains the trace of the squared density matrix. That this corresponds to its 2-norm can be seen when taking M = M † a self-adjoint matrix. Eq. (4) then becomes ...
... The 2-norm is the best suited norm for many computations. One example making use of the 2-norm has already been mentioned. Eq. (1) contains the trace of the squared density matrix. That this corresponds to its 2-norm can be seen when taking M = M † a self-adjoint matrix. Eq. (4) then becomes ...
Introduction to quantum mechanics, Part II
... 20.2 The zero potential case . . . . . . . . . . . . . . . . . . . . . . . . 191 20.2.1 The non-relativistic zero potential case . . . . . . . . . . . 191 ...
... 20.2 The zero potential case . . . . . . . . . . . . . . . . . . . . . . . . 191 20.2.1 The non-relativistic zero potential case . . . . . . . . . . . 191 ...
Noncommutative geometry and reality
... This minor modification allows to treat locally compact spaces as well. After these general preliminaries we shall now give two examples. The first example will simply show that a Riemannian spin manifold M defines a canonical spectral triple as follows: We let X be the Hilbert space L2(M,S) of squa ...
... This minor modification allows to treat locally compact spaces as well. After these general preliminaries we shall now give two examples. The first example will simply show that a Riemannian spin manifold M defines a canonical spectral triple as follows: We let X be the Hilbert space L2(M,S) of squa ...
2. Fundamental principles
... coefficients cn ) we may also construct a wavefunction Ψ(x, t) with the form of a wavepacket which mimics the classical motion of a particle which bounces back and forth between the two hard walls. You will find such an animation in the Matlab program “wavepacket in box”. Some of the “moral” of this ...
... coefficients cn ) we may also construct a wavefunction Ψ(x, t) with the form of a wavepacket which mimics the classical motion of a particle which bounces back and forth between the two hard walls. You will find such an animation in the Matlab program “wavepacket in box”. Some of the “moral” of this ...
Introduction to Representations of the Canonical Commutation and
... the CAR over a given Euclidean space [17]. If this Euclidean space is of countably infinite dimension, the C ∗ -algebra of the CAR is isomorphic to the so called U HF (2∞ ) algebra studied by Glimm. Using representations of this C ∗ -algebra one can construct various non-isomorphic kinds of factors ( ...
... the CAR over a given Euclidean space [17]. If this Euclidean space is of countably infinite dimension, the C ∗ -algebra of the CAR is isomorphic to the so called U HF (2∞ ) algebra studied by Glimm. Using representations of this C ∗ -algebra one can construct various non-isomorphic kinds of factors ( ...
tions processing as well as in quantum information processing. In anal
... Quantum systems have many possible states all of which obey the principle of superposition. The set of all states of an isolated quantum system thus forms a linear vector space over the complex numbers, the Hilbert space. (Note that we are discussing exclusively pure states right now. Mixed states w ...
... Quantum systems have many possible states all of which obey the principle of superposition. The set of all states of an isolated quantum system thus forms a linear vector space over the complex numbers, the Hilbert space. (Note that we are discussing exclusively pure states right now. Mixed states w ...