HWU4-21 QUESTION: The principal quantum number, n, describes
... The principal quantum number, n, describes the energy level of a particular orbital as a function of the distance from the center of the nucleus. Additional quantum numbers exist to quantify the other characteristics of the electron. The angular momentum quantum number (ℓ), the magnetic quantum numb ...
... The principal quantum number, n, describes the energy level of a particular orbital as a function of the distance from the center of the nucleus. Additional quantum numbers exist to quantify the other characteristics of the electron. The angular momentum quantum number (ℓ), the magnetic quantum numb ...
Set #5 - comsics
... 9. A particle in an infinite well is in the ground state with an energy of 1.26 eV. How much energy must be added to the particle to reach the second excited state (n = 3)? The third excited state (n = 4)? (Krane, P4, pg. 170) 10. An electron is trapped in a one-dimensional well of width 0.132 nm. T ...
... 9. A particle in an infinite well is in the ground state with an energy of 1.26 eV. How much energy must be added to the particle to reach the second excited state (n = 3)? The third excited state (n = 4)? (Krane, P4, pg. 170) 10. An electron is trapped in a one-dimensional well of width 0.132 nm. T ...
phys3313-fall13
... 3) For finite potentials, the wave function and its derivatives must be continuous. This is required because the second-order derivative term in the wave equation must be single valued. (There are exceptions to this rule when V is infinite.) 4) In order to normalize the wave functions, they must app ...
... 3) For finite potentials, the wave function and its derivatives must be continuous. This is required because the second-order derivative term in the wave equation must be single valued. (There are exceptions to this rule when V is infinite.) 4) In order to normalize the wave functions, they must app ...
Copenhagen Interpretation (of quantum physics)
... The key concept is the so-called ‘collapse of the wave function’, In seeking to explain how an entity such as a photon or an electron could ‘travel as a wave but arrive as a particle’, Bohr and his colleagues said it was the act of observing the wave that made it ‘collapse’ to become a particle… But ...
... The key concept is the so-called ‘collapse of the wave function’, In seeking to explain how an entity such as a photon or an electron could ‘travel as a wave but arrive as a particle’, Bohr and his colleagues said it was the act of observing the wave that made it ‘collapse’ to become a particle… But ...
Chapter 3 Wave Properties of Particles Overview
... λ= (46×10-3 kg)× 30 m/s λ = 4.8×10-34 m Tell me something that has a physical dimension on the order of 10-34 m, which the golf ball wave could interact with? Can we do an experiment which would detect the golf ball wave? ...
... λ= (46×10-3 kg)× 30 m/s λ = 4.8×10-34 m Tell me something that has a physical dimension on the order of 10-34 m, which the golf ball wave could interact with? Can we do an experiment which would detect the golf ball wave? ...
Chapter 4 Introduction to many
... For sake of simplicity and concreteness we will now assume that the L basis functions |φi i of the single particle Hilbert space factor into L/(2S + 1) orbital wave functions fi (~q) and 2S + 1 spin wave functions |σi, where σ = −S, −S + 1, ..., S. We will write creation and annihilation operators a ...
... For sake of simplicity and concreteness we will now assume that the L basis functions |φi i of the single particle Hilbert space factor into L/(2S + 1) orbital wave functions fi (~q) and 2S + 1 spin wave functions |σi, where σ = −S, −S + 1, ..., S. We will write creation and annihilation operators a ...
PART 1 Identical particles, fermions and bosons. Pauli exclusion
... Here ϕ1 and ϕ2 are spin wave functions of the first and the second nucleus respectively. U is the wave function of the center of mass motion. V is the wave function of the relative motion. Spin of the nucleus is zero, S = 0. Hence ϕ1 = ϕ2 = 1. V (~r1 − ~r2 ) = χ(| r~1 − r~2 |)Ylm (~ r1 − r~2 ) ...
... Here ϕ1 and ϕ2 are spin wave functions of the first and the second nucleus respectively. U is the wave function of the center of mass motion. V is the wave function of the relative motion. Spin of the nucleus is zero, S = 0. Hence ϕ1 = ϕ2 = 1. V (~r1 − ~r2 ) = χ(| r~1 − r~2 |)Ylm (~ r1 − r~2 ) ...
Main postulates
... Both functions are continuous and defined on the interval of interest. They are both single valued and differentiable. However, consider the integral of x: ...
... Both functions are continuous and defined on the interval of interest. They are both single valued and differentiable. However, consider the integral of x: ...
Read Notes #1 - Faculty Website Listing
... What is important is that you understand how radically our picture of the world has changed. Classical Physics is DETERMINISTIC. In Classical physics it is possible at least theoretically for one to specify exactly both the position and velocity of a particle (i.e. its trajectory). This is what you ...
... What is important is that you understand how radically our picture of the world has changed. Classical Physics is DETERMINISTIC. In Classical physics it is possible at least theoretically for one to specify exactly both the position and velocity of a particle (i.e. its trajectory). This is what you ...
x - Piazza
... Time-Independent Schrödinger Wave Equation The potential in many cases will not depend explicitly on time: V = V(x). The Schrödinger equation’s dependence on time and position can then be separated. Let: ...
... Time-Independent Schrödinger Wave Equation The potential in many cases will not depend explicitly on time: V = V(x). The Schrödinger equation’s dependence on time and position can then be separated. Let: ...
Homework Set 1
... An operator  is Hermitian on a space of functions F if (i) the operator  has real eigenvalues, and (ii) if operating  on functions in F gives back functions in F. For the problem below, we shall consider F to comprise all smooth, real and bounded functions in 1d space. (Bounded simply means th ...
... An operator  is Hermitian on a space of functions F if (i) the operator  has real eigenvalues, and (ii) if operating  on functions in F gives back functions in F. For the problem below, we shall consider F to comprise all smooth, real and bounded functions in 1d space. (Bounded simply means th ...
Quantum Electrodynamics
... among the greatest triumphs in theoretical physics. Later, Feynman came up with an alternative interpretation of positrons as electrons traveling backward in time. This led to great simplification of the theory, which came to be known as quantum electrodynamics. So, to modify the Klein-Gordon equati ...
... among the greatest triumphs in theoretical physics. Later, Feynman came up with an alternative interpretation of positrons as electrons traveling backward in time. This led to great simplification of the theory, which came to be known as quantum electrodynamics. So, to modify the Klein-Gordon equati ...
Wave function
A wave function in quantum mechanics describes the quantum state of an isolated system of one or more particles. There is one wave function containing all the information about the entire system, not a separate wave function for each particle in the system. Its interpretation is that of a probability amplitude. Quantities associated with measurements, such as the average momentum of a particle, can be derived from the wave function. It is a central entity in quantum mechanics and is important in all modern theories, like quantum field theory incorporating quantum mechanics, while its interpretation may differ. The most common symbols for a wave function are the Greek letters ψ or Ψ (lower-case and capital psi).For a given system, once a representation corresponding to a maximal set of commuting observables and a suitable coordinate system is chosen, the wave function is a complex-valued function of the system's degrees of freedom corresponding to the chosen representation and coordinate system, continuous as well as discrete. Such a set of observables, by a postulate of quantum mechanics, are Hermitian linear operators on the space of states representing a set of physical observables, like position, momentum and spin that can, in principle, be simultaneously measured with arbitrary precision. Wave functions can be added together and multiplied by complex numbers to form new wave functions, and hence are elements of a vector space. This is the superposition principle of quantum mechanics. This vector space is endowed with an inner product such that it is a complete metric topological space with respect to the metric induced by the inner product. In this way the set of wave functions for a system form a function space that is a Hilbert space. The inner product is a measure of the overlap between physical states and is used in the foundational probabilistic interpretation of quantum mechanics, the Born rule, relating transition probabilities to inner products. The actual space depends on the system's degrees of freedom (hence on the chosen representation and coordinate system) and the exact form of the Hamiltonian entering the equation governing the dynamical behavior. In the non-relativistic case, disregarding spin, this is the Schrödinger equation.The Schrödinger equation determines the allowed wave functions for the system and how they evolve over time. A wave function behaves qualitatively like other waves, such as water waves or waves on a string, because the Schrödinger equation is mathematically a type of wave equation. This explains the name ""wave function"", and gives rise to wave–particle duality. The wave of the wave function, however, is not a wave in physical space; it is a wave in an abstract mathematical ""space"", and in this respect it differs fundamentally from water waves or waves on a string.For a given system, the choice of which relevant degrees of freedom to use are not unique, and correspondingly the domain of the wave function is not unique. It may be taken to be a function of all the position coordinates of the particles over position space, or the momenta of all the particles over momentum space, the two are related by a Fourier transform. These descriptions are the most important, but they are not the only possibilities. Just like in classical mechanics, canonical transformations may be used in the description of a quantum system. Some particles, like electrons and photons, have nonzero spin, and the wave function must include this fundamental property as an intrinsic discrete degree of freedom. In general, for a particle with half-integer spin the wave function is a spinor, for a particle with integer spin the wave function is a tensor. Particles with spin zero are called scalar particles, those with spin 1 vector particles, and more generally for higher integer spin, tensor particles. The terminology derives from how the wave functions transform under a rotation of the coordinate system. No elementary particle with spin 3⁄2 or higher is known, except for the hypothesized spin 2 graviton. Other discrete variables can be included, such as isospin. When a system has internal degrees of freedom, the wave function at each point in the continuous degrees of freedom (e.g. a point in space) assigns a complex number for each possible value of the discrete degrees of freedom (e.g. z-component of spin). These values are often displayed in a column matrix (e.g. a 2 × 1 column vector for a non-relativistic electron with spin 1⁄2).In the Copenhagen interpretation, an interpretation of quantum mechanics, the squared modulus of the wave function, |ψ|2, is a real number interpreted as the probability density of measuring a particle as being at a given place at a given time or having a definite momentum, and possibly having definite values for discrete degrees of freedom. The integral of this quantity, over all the system's degrees of freedom, must be 1 in accordance with the probability interpretation, this general requirement a wave function must satisfy is called the normalization condition. Since the wave function is complex valued, only its relative phase and relative magnitude can be measured. Its value does not in isolation tell anything about the magnitudes or directions of measurable observables; one has to apply quantum operators, whose eigenvalues correspond to sets of possible results of measurements, to the wave function ψ and calculate the statistical distributions for measurable quantities.The unit of measurement for ψ depends on the system, and can be found by dimensional analysis of the normalization condition for the system. For one particle in three dimensions, its units are [length]−3/2, because an integral of |ψ|2 over a region of three-dimensional space is a dimensionless probability.