Physicists realize an atom laser, a source of coherent matter waves
... many-body wavefunction is still, to a very good approximation, a product of N single-particle wavefunctions, which are now obtained from the solution of a non-linear Schrödinger equation, which includes the interaction energy between atoms. The admixture of other configurations into the ground stat ...
... many-body wavefunction is still, to a very good approximation, a product of N single-particle wavefunctions, which are now obtained from the solution of a non-linear Schrödinger equation, which includes the interaction energy between atoms. The admixture of other configurations into the ground stat ...
Revision of Boltzmann statistics for a finite number of particles
... dependence of the parameters Wm, NW, and ZW for which the Lambert-Boltzmann distribution in Eq. 共19兲 applies. D. Exact solution of the Boltzmann problem in terms of the inverse Digamma-function The exact derivative of ln共n!兲 is given by the Digammafunction 0: d ln共n!兲 / dn = 0共n + 1兲, where the a ...
... dependence of the parameters Wm, NW, and ZW for which the Lambert-Boltzmann distribution in Eq. 共19兲 applies. D. Exact solution of the Boltzmann problem in terms of the inverse Digamma-function The exact derivative of ln共n!兲 is given by the Digammafunction 0: d ln共n!兲 / dn = 0共n + 1兲, where the a ...
Chemical potential of one-dimensional simple harmonic oscillators
... Of the various terms in equation (1), probably μ is the least familiar to undergraduate students being introduced to thermodynamics for the first time [3, 4]. Part of the reason may be that there are few examples of analytic calculations of μ for a system of particles other than for a classical ideal ...
... Of the various terms in equation (1), probably μ is the least familiar to undergraduate students being introduced to thermodynamics for the first time [3, 4]. Part of the reason may be that there are few examples of analytic calculations of μ for a system of particles other than for a classical ideal ...
Lactose Free, Direct Compression Formulation Used to Produce
... an allergic reaction. Many marketed loratadine products use lactose as the main filler ingredient. Lactose, one of the most commonly used fillers in solid dosage formulations, is well known for producing tablets with high mechanical strength. However, its usage has been eroded by some relatively rec ...
... an allergic reaction. Many marketed loratadine products use lactose as the main filler ingredient. Lactose, one of the most commonly used fillers in solid dosage formulations, is well known for producing tablets with high mechanical strength. However, its usage has been eroded by some relatively rec ...
Quantum Statistics - Ole Witt
... The task of classical statistical mechanics is to give a theoretical foundation of the empirical laws of thermodynamics, and enable us to compute the functions of state, i.e. temperature T, pressure P, energy E and entropy S , when the mechanical constitution of the system is statistically defined. ...
... The task of classical statistical mechanics is to give a theoretical foundation of the empirical laws of thermodynamics, and enable us to compute the functions of state, i.e. temperature T, pressure P, energy E and entropy S , when the mechanical constitution of the system is statistically defined. ...
Classical and Quantum Ideal Gases
... Fermions Soon after Bose and Einstein’s work, Fermi and Dirac developed FermiDirac statistics for fermions. Fermions possess half-integer spin, and include electrons, protons and neutrons. Fermions obey the Pauli exclusion principle (Pauli, 1925), which states that two identical fermions cannot occu ...
... Fermions Soon after Bose and Einstein’s work, Fermi and Dirac developed FermiDirac statistics for fermions. Fermions possess half-integer spin, and include electrons, protons and neutrons. Fermions obey the Pauli exclusion principle (Pauli, 1925), which states that two identical fermions cannot occu ...
Moles, Atoms, Molecules 10C
... The atomic mass is found by checking the periodic table. The atomic mass is the number of grams of an element that is numerically equal to the mass of an atomic mass unit. atomic mass C = 12.0 g The atomic mass is the mass of one mole of atoms. Mole – quantity such that there are as many atoms as in ...
... The atomic mass is found by checking the periodic table. The atomic mass is the number of grams of an element that is numerically equal to the mass of an atomic mass unit. atomic mass C = 12.0 g The atomic mass is the mass of one mole of atoms. Mole – quantity such that there are as many atoms as in ...
Mole-notes
... DETERMINING THE HYDRATE’S FORMULA It is a lot like calculating the empirical formula only you are not using single elements. You are using water and the compound. Follow these steps You have a 5.00g sample of a barium chloride hydrate. Determine the correct formula is you are given 5.00g of the hydr ...
... DETERMINING THE HYDRATE’S FORMULA It is a lot like calculating the empirical formula only you are not using single elements. You are using water and the compound. Follow these steps You have a 5.00g sample of a barium chloride hydrate. Determine the correct formula is you are given 5.00g of the hydr ...
The Mole: A Measurement of Matter
... If the numbers are both whole numbers, these will be the subscripts of the elements in the formula If the whole numbers are identical, substitute the number 1 Example: C2H2 and C8H8 have an empirical formula of CH If either or both numbers are not whole numbers, numbers in the ratio must be multipli ...
... If the numbers are both whole numbers, these will be the subscripts of the elements in the formula If the whole numbers are identical, substitute the number 1 Example: C2H2 and C8H8 have an empirical formula of CH If either or both numbers are not whole numbers, numbers in the ratio must be multipli ...
The non-interacting Bose gas
... holds for a system that is in contact with a large reservoir, such that it can exchange energy and particles with the reservoir. The constants in this ensemble are the chemical potential µ and the temperature T . Applying the concept of the grand canonical ensemble to trapped gases is valid under th ...
... holds for a system that is in contact with a large reservoir, such that it can exchange energy and particles with the reservoir. The constants in this ensemble are the chemical potential µ and the temperature T . Applying the concept of the grand canonical ensemble to trapped gases is valid under th ...
Objectives: • Explain work in mechanical systems • Solve math
... a. Write the formula to find efficiency (1pt) _____________________________ b. Put the numbers and labels in the formula (1pt) _____________________ c. Write the correct answer and label (2 pts) _______________________ 6. A person uses a lever to raise a 400 Newton box up a distance of 0.5 meters. T ...
... a. Write the formula to find efficiency (1pt) _____________________________ b. Put the numbers and labels in the formula (1pt) _____________________ c. Write the correct answer and label (2 pts) _______________________ 6. A person uses a lever to raise a 400 Newton box up a distance of 0.5 meters. T ...
Helium - NICADD
... practically only need to worry about valence effects. Solids, different terms lead to energy bands ...
... practically only need to worry about valence effects. Solids, different terms lead to energy bands ...
Many Particle Systems
... practically only need to worry about valence effects. Solids, different terms lead to energy bands ...
... practically only need to worry about valence effects. Solids, different terms lead to energy bands ...
Lecture 7
... When the temperature increases, excited states become populated. The question that we would like to find an answer to is the following: If we have a large number of particles N in thermal equilibrium at temperature T, what is the probability that randomly selected particle has specific energy Ei? We ...
... When the temperature increases, excited states become populated. The question that we would like to find an answer to is the following: If we have a large number of particles N in thermal equilibrium at temperature T, what is the probability that randomly selected particle has specific energy Ei? We ...
The Spin-Statistics Theorem and Identical Particle
... varied. Let us illustrate their use in Bose-Einstein condensation (BEC). Its story begins in 1924 when Satyendra Bose sent to Albert Einstein a paper about counting the quantum states of photons. Bose had trouble getting his paper accepted, but Einstein was impressed, translated the paper from Engli ...
... varied. Let us illustrate their use in Bose-Einstein condensation (BEC). Its story begins in 1924 when Satyendra Bose sent to Albert Einstein a paper about counting the quantum states of photons. Bose had trouble getting his paper accepted, but Einstein was impressed, translated the paper from Engli ...
Identical particles
... Elementary particles have spin, which is the name that we give to the intrinsic angular momentum of the particle. It is the angular momentum that the particle has that does not come from its motion via the orbital angular momentum L = r × p . The symbol used for spin is usually s or S. Like orbital ...
... Elementary particles have spin, which is the name that we give to the intrinsic angular momentum of the particle. It is the angular momentum that the particle has that does not come from its motion via the orbital angular momentum L = r × p . The symbol used for spin is usually s or S. Like orbital ...
Ensembles(b)
... Here, Qi denotes collectively all the coordinates of the i particle (i.e. its position and spin coordinates if any). The possible quantum states are labelled by the indices si. Two cases need to be considered. In the classical case (Maxwell-Boltzmann statistics), the particles are considered disting ...
... Here, Qi denotes collectively all the coordinates of the i particle (i.e. its position and spin coordinates if any). The possible quantum states are labelled by the indices si. Two cases need to be considered. In the classical case (Maxwell-Boltzmann statistics), the particles are considered disting ...
Atomic Mass - MsReenChemistry
... The mass of product deposited on an electrode can be calculated because 1 Faraday is 1 m______ of e_________ The first thing to do is to work out how many coulombs of electricity flowed during the electrolysis. Number of coulombs = current in amps x time in seconds Number of coulombs = 0.10 x 10 x 6 ...
... The mass of product deposited on an electrode can be calculated because 1 Faraday is 1 m______ of e_________ The first thing to do is to work out how many coulombs of electricity flowed during the electrolysis. Number of coulombs = current in amps x time in seconds Number of coulombs = 0.10 x 10 x 6 ...
Identical Particles ( + problems 34
... where m is the mass of the atom, and c is the velocity of light. Looking at Eq. (7), we note that if not for the constraint (6), each single-particle mode could be considered as an independent subsystem. We also see that in the case of bosons, where nk = 0, 1, 2, . . . each single-mode subsystem is ...
... where m is the mass of the atom, and c is the velocity of light. Looking at Eq. (7), we note that if not for the constraint (6), each single-particle mode could be considered as an independent subsystem. We also see that in the case of bosons, where nk = 0, 1, 2, . . . each single-mode subsystem is ...
Chemical Quantities - Malibu High School
... 3b. Students know the quantity of one mole is set by defining one mole of carbon-12 atoms to have a mass of exactly 12 grams. 3c. Students know one mole equals 6.02 x 1023 particles (atoms or molecules). 3d. Students know how to determine the molar mass of a molecule from its chemical formula and a ...
... 3b. Students know the quantity of one mole is set by defining one mole of carbon-12 atoms to have a mass of exactly 12 grams. 3c. Students know one mole equals 6.02 x 1023 particles (atoms or molecules). 3d. Students know how to determine the molar mass of a molecule from its chemical formula and a ...
Pre-AP Chemistry Chemical Quantities Review Sheet
... Chemical Quantities Review Sheet PART 1: THE MOLE AND CONVERSION - A conversion factor allows for the conversion between units. - Representative particle – species present in a substance o Include atoms, molecules, ion, formula units - Conversion Factor 1: 1 mole = 6.02 x 1023 items o Avogadro’s n ...
... Chemical Quantities Review Sheet PART 1: THE MOLE AND CONVERSION - A conversion factor allows for the conversion between units. - Representative particle – species present in a substance o Include atoms, molecules, ion, formula units - Conversion Factor 1: 1 mole = 6.02 x 1023 items o Avogadro’s n ...