Questions from past exam papers. 1. (a) (8 marks) The Hamiltonian
... (i) For the Hamiltonian Ĥ = p̂2 /2m + V( x̂) check that Ĥ, p̂ = i~ dV/dx. (ii) Interpret this result by developing the analogy between classical and quantum mechanics. (b) (6 marks) A quantum system can exist in two states |0i and |1i, which are normalised eigenstates of an observable A with eigen ...
... (i) For the Hamiltonian Ĥ = p̂2 /2m + V( x̂) check that Ĥ, p̂ = i~ dV/dx. (ii) Interpret this result by developing the analogy between classical and quantum mechanics. (b) (6 marks) A quantum system can exist in two states |0i and |1i, which are normalised eigenstates of an observable A with eigen ...
Sources of the Magnetic Field
... The direction of the magnetic field is given by one of the right-hand rules Point your thumb, of your right hand, in the direction of the velocity and curl your fingers. The direction of the field is then the direction your fingers curl. The magnetic field for a negative charge will be in the opposi ...
... The direction of the magnetic field is given by one of the right-hand rules Point your thumb, of your right hand, in the direction of the velocity and curl your fingers. The direction of the field is then the direction your fingers curl. The magnetic field for a negative charge will be in the opposi ...
Applications of Supersymmetric Quantum
... after its very founder M.V.Berry). We shall see that during a cycling quantum evolution the phase change has two parts: the usual dynamical part and the geometric part, which is of our interest here, because it can have observable consequences. Let me start with some fundamentals from one dimensiona ...
... after its very founder M.V.Berry). We shall see that during a cycling quantum evolution the phase change has two parts: the usual dynamical part and the geometric part, which is of our interest here, because it can have observable consequences. Let me start with some fundamentals from one dimensiona ...
Chapter 28
... Given a path around which the integration is to be done, there is a sign convention for the current Determine the direction of the normal, as defined by the sense of movement around the integration path If the current is going in the same direction as the normal, the current is considered to be posi ...
... Given a path around which the integration is to be done, there is a sign convention for the current Determine the direction of the normal, as defined by the sense of movement around the integration path If the current is going in the same direction as the normal, the current is considered to be posi ...
Multidimensional Hypergeometric Functions in Conformai Field
... (ßL = dln(z1/z0) over a path going from M1 to M 0 . flj(L;M) is equal to the logarithm of the cross ratio of the four points (L 0 , Ll9 M0, Mx). The Euler dilogarithm is a special case of the Aomoto dilogarithm, see Fig. 1. There are two connections of polylogarithms of different orders: the multipl ...
... (ßL = dln(z1/z0) over a path going from M1 to M 0 . flj(L;M) is equal to the logarithm of the cross ratio of the four points (L 0 , Ll9 M0, Mx). The Euler dilogarithm is a special case of the Aomoto dilogarithm, see Fig. 1. There are two connections of polylogarithms of different orders: the multipl ...
The evolution of free wave packets
... out without limit. How different this behavior is from that of a free classical particle. The reconciliation of the classical and quantum descriptions is part of the bigger question of the interpretation of quantum mechanics; here we will consider only the dynamics of free wave packets as given by S ...
... out without limit. How different this behavior is from that of a free classical particle. The reconciliation of the classical and quantum descriptions is part of the bigger question of the interpretation of quantum mechanics; here we will consider only the dynamics of free wave packets as given by S ...
What classicality? Decoherence and Bohr`s classical concepts
... environmental degrees of freedom. Quantum mechanics tells us how to compute the statistics of all possible measurements on the system: we need to simply “trace out” the environment in the system–environment density matrix. And what pops out is the reduced density matrix, which is the main object of ...
... environmental degrees of freedom. Quantum mechanics tells us how to compute the statistics of all possible measurements on the system: we need to simply “trace out” the environment in the system–environment density matrix. And what pops out is the reduced density matrix, which is the main object of ...
Square-root measurement for quantum
... the suboptimum quantum receiver [1]. In the Helstrom’s iterative procedure of the Bayes-cost reduction [8] and the other numerical calculation methods [21]–[23], the SRM is used to give the initial measurement process. After the paper of Helstrom’s iterative algorithm, the SRM has been investigated ...
... the suboptimum quantum receiver [1]. In the Helstrom’s iterative procedure of the Bayes-cost reduction [8] and the other numerical calculation methods [21]–[23], the SRM is used to give the initial measurement process. After the paper of Helstrom’s iterative algorithm, the SRM has been investigated ...
The principle of relativity and the De Broglie relation - Loreto
... major, in a curricular unit of introduction to modern physics. At that stage, students are generally not yet acquainted with the relativistic formalism (or even with relativity at all). Therefore we accept the way in which the De Broglie relation is usually taught, but we claim that, in a later stag ...
... major, in a curricular unit of introduction to modern physics. At that stage, students are generally not yet acquainted with the relativistic formalism (or even with relativity at all). Therefore we accept the way in which the De Broglie relation is usually taught, but we claim that, in a later stag ...
Quantum-like model of unconscious–conscious dynamics
... a complex linear space endowed with a scalar product, a positivedefinite non-degenerate Hermitian form.√Denote the latter by h·|·i. It generates the norm on H : kψk = hψ|ψi. A reader who does not feel comfortable in the abstract framework of functional analysis can simply proceed with the Hilbert sp ...
... a complex linear space endowed with a scalar product, a positivedefinite non-degenerate Hermitian form.√Denote the latter by h·|·i. It generates the norm on H : kψk = hψ|ψi. A reader who does not feel comfortable in the abstract framework of functional analysis can simply proceed with the Hilbert sp ...
Notes on 2d quantum gravity and Liouville theory - lpthe
... 5.1.2 Adding the cosmological constant term . . . . . . . . . . . . . . . . 5.2 Derivation of the classical Liouville action . . . . . . . . . . . . . . . . . . 5.2.1 Integrating the conformal anomaly . . . . . . . . . . . . . . . . . . 5.2.2 Partition function and transformation properties . . . . ...
... 5.1.2 Adding the cosmological constant term . . . . . . . . . . . . . . . . 5.2 Derivation of the classical Liouville action . . . . . . . . . . . . . . . . . . 5.2.1 Integrating the conformal anomaly . . . . . . . . . . . . . . . . . . 5.2.2 Partition function and transformation properties . . . . ...
Schumacher Compression
... the receiver reproduces the classical sequence x n at his end, and finally reconstructs the sequence ∣ψ x n ⟩ of quantum states corresponding to the classical sequence x n . The above strategy will certainly work, but it makes no use of the fact that the noiseless quantum channels are quantum! It is ...
... the receiver reproduces the classical sequence x n at his end, and finally reconstructs the sequence ∣ψ x n ⟩ of quantum states corresponding to the classical sequence x n . The above strategy will certainly work, but it makes no use of the fact that the noiseless quantum channels are quantum! It is ...
Mathematical Fundamentals
... charge states that the total charge (algebraic sum of positive and negative charges) of an isolated system remains unchanged, though the charges may redistribute under the influence of electric field. Kirchhoff's Current Law (KCL) is an assertion of the conservative property of charges under the imp ...
... charge states that the total charge (algebraic sum of positive and negative charges) of an isolated system remains unchanged, though the charges may redistribute under the influence of electric field. Kirchhoff's Current Law (KCL) is an assertion of the conservative property of charges under the imp ...
Self-consistent approach for calculations of exciton binding energy
... applications require more flexible, accurate and effective methods. Presently, the best results are usually obtained within the framework of the variational approach, where a certain form of the exciton wave function, depending on one or more variational parameters is being postulated. The exciton en ...
... applications require more flexible, accurate and effective methods. Presently, the best results are usually obtained within the framework of the variational approach, where a certain form of the exciton wave function, depending on one or more variational parameters is being postulated. The exciton en ...
Physlets and Open Source Physics for Quantum Mechanics:
... applications, but fails for more sophisticated one-of-a-kind simulations that require advanced discipline-specific expertise, such as those for quantum mechanics. Users and developers of these types of programs often have specialized curricular needs that can only be addressed by having access to th ...
... applications, but fails for more sophisticated one-of-a-kind simulations that require advanced discipline-specific expertise, such as those for quantum mechanics. Users and developers of these types of programs often have specialized curricular needs that can only be addressed by having access to th ...
Million-Atom Pseudopotential Calculation of GX Mixing in GaAs AlAs
... The crossover from direct band gap to indirect band gap (e.g., G ! X) as a function of an external parameter is common in semiconductor physics. It is seen in (i) zinc blende materials (GaAs [1], InP [2]) as a function of pressure, (ii) alloys (Alx Ga12x As [3], Gax In12x P [4]) as a function of com ...
... The crossover from direct band gap to indirect band gap (e.g., G ! X) as a function of an external parameter is common in semiconductor physics. It is seen in (i) zinc blende materials (GaAs [1], InP [2]) as a function of pressure, (ii) alloys (Alx Ga12x As [3], Gax In12x P [4]) as a function of com ...
Lecture Notes: Condensed Matter Theory I (TKM1)
... molecules in liquid or solid form. It is one of the largest branches of physics, with a wide variety of di¤erent systems, approaches, challenges and concepts. Often, it is subdivided in soft condensed matter physics and hard condensed matter physics. While the transition between the two branches is ...
... molecules in liquid or solid form. It is one of the largest branches of physics, with a wide variety of di¤erent systems, approaches, challenges and concepts. Often, it is subdivided in soft condensed matter physics and hard condensed matter physics. While the transition between the two branches is ...
