Wavefunctions and Bound Systems
... probability distributions (Born interpretation) • Wavefunctions can be described using the mathematics of waves but are not “real” • Wavefunctions obey strict mathematical rules: – continuous, differentiable, finite ...
... probability distributions (Born interpretation) • Wavefunctions can be described using the mathematics of waves but are not “real” • Wavefunctions obey strict mathematical rules: – continuous, differentiable, finite ...
6. Quantum Mechanics II
... which is a sine wave moving in the x direction. Notice that, unlike classical waves, we are not taking the real part of this function. is, in fact, complex. In general, the wave function is complex. But the physically measurable quantities must be real. These include the probability, position, mom ...
... which is a sine wave moving in the x direction. Notice that, unlike classical waves, we are not taking the real part of this function. is, in fact, complex. In general, the wave function is complex. But the physically measurable quantities must be real. These include the probability, position, mom ...
lecture 7
... • We want to obtain the energy of the hydrogen atom system. We will do this the same way as we got it for the particle-in-a-box: by performing the “energy operation” on the wavefunction which describes the H atom system. ...
... • We want to obtain the energy of the hydrogen atom system. We will do this the same way as we got it for the particle-in-a-box: by performing the “energy operation” on the wavefunction which describes the H atom system. ...
Exercises in Statistical Mechanics
... A cylinder of of radius R rotates about its axis with a constant angular velocity Ω. It contains an ideal classical gas of N particles at temperature T . Find the density distribution as a function of the radial distance from the axis. Write what is the pressure on the walls. Note that the Hamiltoni ...
... A cylinder of of radius R rotates about its axis with a constant angular velocity Ω. It contains an ideal classical gas of N particles at temperature T . Find the density distribution as a function of the radial distance from the axis. Write what is the pressure on the walls. Note that the Hamiltoni ...
quantum1
... events will behave in a statistically predictable way. probability for an electron to be found between x and x+dx ...
... events will behave in a statistically predictable way. probability for an electron to be found between x and x+dx ...
Lecture 8 - Pauli exclusion principle, particle in a box, Heisenberg
... have two possible values of spin (+½ or -½), so the Pauli exclusion principle in fact demands unique values of x s , where s is a spinor describing the spin of a particle. ...
... have two possible values of spin (+½ or -½), so the Pauli exclusion principle in fact demands unique values of x s , where s is a spinor describing the spin of a particle. ...
Slide 1
... Electrons don’t move at the speed of light (although in certain cases they can be close), so rearrange the equation for the mass of the photon to solve for the momentum of the electrons using “v” as the velocity of the electron ...
... Electrons don’t move at the speed of light (although in certain cases they can be close), so rearrange the equation for the mass of the photon to solve for the momentum of the electrons using “v” as the velocity of the electron ...
Class23
... Quantum mechanics challenges our physical intuition but it is the way things really work. Particles are described with a wave function Y(x,t) which describes the propagation through space and time (when unobserved). ...
... Quantum mechanics challenges our physical intuition but it is the way things really work. Particles are described with a wave function Y(x,t) which describes the propagation through space and time (when unobserved). ...
8.04 Final Review Schr¨ ary conditions.
... Some important commutator results are [x̂, p̂] = i~, and [Â, Aˆ+ ] = 1. TODO: (need more here about Hermitians, conjugate adjoints and how they work backwards on dirac notation etc.) TODO: Dirac notation ...
... Some important commutator results are [x̂, p̂] = i~, and [Â, Aˆ+ ] = 1. TODO: (need more here about Hermitians, conjugate adjoints and how they work backwards on dirac notation etc.) TODO: Dirac notation ...
Notes - Particle Theory
... – we define this as the zero energy, zero charge state – a hole in this “sea” of negative energy states has positive energy and the opposite charge: it is an anti-particle – a partice/anti-particle pair can be created out of energy when a particle moves from a negative energy state into a positive e ...
... – we define this as the zero energy, zero charge state – a hole in this “sea” of negative energy states has positive energy and the opposite charge: it is an anti-particle – a partice/anti-particle pair can be created out of energy when a particle moves from a negative energy state into a positive e ...
Q.M3 Home work 9 Due date 3.1.15 1
... A coherent state is the specific quantum state of the quantum harmonic oscillator whose dynamics most closely resembles the oscillating behaviour of a classical harmonic oscillator. Further, in contrast to the energy eigenstates of the system, the time evolution of a coherent state is concentrated a ...
... A coherent state is the specific quantum state of the quantum harmonic oscillator whose dynamics most closely resembles the oscillating behaviour of a classical harmonic oscillator. Further, in contrast to the energy eigenstates of the system, the time evolution of a coherent state is concentrated a ...
4.1 Schr¨ odinger Equation in Spherical Coordinates ~
... similar types of motion. Experiments have shown that the behavior of electrons in magnetic fields, for example, cannot be explained without invoking the existence of a constant of motion in addition to the energy and momentum. It apparently must be characterized by an intrinsic angular momentum S, o ...
... similar types of motion. Experiments have shown that the behavior of electrons in magnetic fields, for example, cannot be explained without invoking the existence of a constant of motion in addition to the energy and momentum. It apparently must be characterized by an intrinsic angular momentum S, o ...
Problems for particle physics course:
... 1. ParticleA at rest , decays into particles B and C a) Find the energy of the outgoing particles, in terms of the various masses. b) Find the magnitudes of the outgoing momenta. 2. ParticleA(energy E) hits particle B (at rest), producing particles C1, C2, …, Cn: A+B C1 + C2 + … + Cn. Calculate th ...
... 1. ParticleA at rest , decays into particles B and C a) Find the energy of the outgoing particles, in terms of the various masses. b) Find the magnitudes of the outgoing momenta. 2. ParticleA(energy E) hits particle B (at rest), producing particles C1, C2, …, Cn: A+B C1 + C2 + … + Cn. Calculate th ...
Notes
... lines. For instance, if Δ 1 the transition is forbidden and occurs with very low probability. The photon carries away the angular momentum lost in the allowed transition as spin. For complex atoms, we invoke the Pauli exclusion principle: no two electrons in an atom can occupy the same quantum s ...
... lines. For instance, if Δ 1 the transition is forbidden and occurs with very low probability. The photon carries away the angular momentum lost in the allowed transition as spin. For complex atoms, we invoke the Pauli exclusion principle: no two electrons in an atom can occupy the same quantum s ...
Problem set 6
... 1. Consider a free non-relativistic particle of mass m. In the lecture we assumed the time evolution of each Fourier component of a matter wave ψ(x, t) was given by ei(kx−ω(k)t) corresponding to a right moving wave if k, ω(k) were of the same sign. We could equally well have considered the time evol ...
... 1. Consider a free non-relativistic particle of mass m. In the lecture we assumed the time evolution of each Fourier component of a matter wave ψ(x, t) was given by ei(kx−ω(k)t) corresponding to a right moving wave if k, ω(k) were of the same sign. We could equally well have considered the time evol ...
Pre-class 11
... – Time dilation & Length contraction, events in spacetime Lorentz transformation – Spacetime interval (invariant under LT) – Relativistic forces, momentum and energy – Lot's of applications (and lot's of firecrackers) ...
... – Time dilation & Length contraction, events in spacetime Lorentz transformation – Spacetime interval (invariant under LT) – Relativistic forces, momentum and energy – Lot's of applications (and lot's of firecrackers) ...