28_lecture_acl
... §28.1 Wave-Particle Duality Light is both wave-like (interference & diffraction) and particle-like (photoelectric effect). Double slit experiment: allow only 1 photon at a time, but: • still makes interference pattern! • can’t determine which slit it will pass thru • can’t determine where it will h ...
... §28.1 Wave-Particle Duality Light is both wave-like (interference & diffraction) and particle-like (photoelectric effect). Double slit experiment: allow only 1 photon at a time, but: • still makes interference pattern! • can’t determine which slit it will pass thru • can’t determine where it will h ...
Quantum Mechanics: PHL555 Tutorial 2
... © Show that the spherical harmonics are also eigenstates of the parity operator. 3. The wavefunction of a particle subjected to a spherically symmetric ...
... © Show that the spherical harmonics are also eigenstates of the parity operator. 3. The wavefunction of a particle subjected to a spherically symmetric ...
Energy
... • A “particle” of light • A “quantum” of light energy • The energy of a given photon depends on the frequency (color) of the light ...
... • A “particle” of light • A “quantum” of light energy • The energy of a given photon depends on the frequency (color) of the light ...
Arrangement of Electrons in Atoms
... Max Planck(1900) explanation: objects emit energy in small packets called quanta ...
... Max Planck(1900) explanation: objects emit energy in small packets called quanta ...
Quantum numbers
... finding the electron at position 1 relative to position 2. If the number is 100, the electron is 100 times more likely to be in position 1 than 2. ...
... finding the electron at position 1 relative to position 2. If the number is 100, the electron is 100 times more likely to be in position 1 than 2. ...
Problem 1. What is the wavelength of a hydrogen atom... sponding to the mean kinetic energy at thermal equilibrium at...
... Problem 1. What is the wavelength of a hydrogen atom moving with a velocity corresponding to the mean kinetic energy at thermal equilibrium at 20 degrees Centigrade? [2 points] Problem 2. If you rewrite the uncertainty relation for a free particle in terms of the uncertainty of its wavelength ∆λ rat ...
... Problem 1. What is the wavelength of a hydrogen atom moving with a velocity corresponding to the mean kinetic energy at thermal equilibrium at 20 degrees Centigrade? [2 points] Problem 2. If you rewrite the uncertainty relation for a free particle in terms of the uncertainty of its wavelength ∆λ rat ...
APCh7MB
... Can only know position or velocity As one is known more precisely, the other is known less precisely Δ x Δ (mv) ≥ h/4π Δ x = uncertainty in the particle’s position Δ (mv) = uncertainty in particle’s momentum h = Planck’s constant Smallest possible uncertainty = h/4π (h/4π)2 = probability distribut ...
... Can only know position or velocity As one is known more precisely, the other is known less precisely Δ x Δ (mv) ≥ h/4π Δ x = uncertainty in the particle’s position Δ (mv) = uncertainty in particle’s momentum h = Planck’s constant Smallest possible uncertainty = h/4π (h/4π)2 = probability distribut ...
Particle in a box
In quantum mechanics, the particle in a box model (also known as the infinite potential well or the infinite square well) describes a particle free to move in a small space surrounded by impenetrable barriers. The model is mainly used as a hypothetical example to illustrate the differences between classical and quantum systems. In classical systems, for example a ball trapped inside a large box, the particle can move at any speed within the box and it is no more likely to be found at one position than another. However, when the well becomes very narrow (on the scale of a few nanometers), quantum effects become important. The particle may only occupy certain positive energy levels. Likewise, it can never have zero energy, meaning that the particle can never ""sit still"". Additionally, it is more likely to be found at certain positions than at others, depending on its energy level. The particle may never be detected at certain positions, known as spatial nodes.The particle in a box model provides one of the very few problems in quantum mechanics which can be solved analytically, without approximations. This means that the observable properties of the particle (such as its energy and position) are related to the mass of the particle and the width of the well by simple mathematical expressions. Due to its simplicity, the model allows insight into quantum effects without the need for complicated mathematics. It is one of the first quantum mechanics problems taught in undergraduate physics courses, and it is commonly used as an approximation for more complicated quantum systems.