Quantum mechaincs Definition and 108 Threads

Homework Statement "Suppose that a hydrogen atom, initially in its ground state, is placed in an oscillating electric field ##\mathcal{E}_0 \cos(\omega t) \mathbf{\hat{z}}##, with ##\hbar \omega \gg -13.6\text{eV}##. Calculate the rate of transitions to the continuum." Homework Equations ##R =...

Hello everyone, I actually have three questions: 1. Am I missing an important detail in my understanding of how the delayed choice quantum eraser experiment is done? 2. How does one account for what takes place in the experiment without using the concept of "retrocausality" (effect before...

Homework Statement I'm reading something in my quantum physics book that says given a wavefunction ψ that is even, if we evaluate its integral from -ε to ε, the integral is 0. How can this be? I thought this is the property of odd functions. Homework Equations ψ=Aekx if x<0 and ψ=Be-kx if x>0...

Homework Statement Given a non-hermitian hamiltonian with V = (Re)V -i(Im)V. By deriving the conservation of probability, it can be shown that the total probability of finding a system/particle decreases exponentially as e(-2*ImV*t)/ħ Homework Equations Schrodinger Eqn, conservation of...

Homework Statement It is a potential barrier with E of the incoming matter wave E>U (greater than the height of the barrier). I have already done a LOT of algebra to get to the point where ##\frac{F}{A}=\frac{2kk'e^{-ikL}}{2kk'cos(k'L)-i(k'^{2}+k^{2})sin(k'L)}## which I won't bother writing...

Homework Statement Using the following expression for the Dirac delta function: $$\delta(k-k')=\frac{1}{2\pi} \int_{-\infty}^{\infty}e^{i(k-k')x} \mathrm{d}x$$ Show that if a position space wave function $$\Psi(x,t)$$ is normalized at time t=0, then it is also true that the corresponding...

I am starting to learn Quantum mechanics. I can't wait for my completion of QM, as I am running behind all the concepts taught in the class; but I can't even go on studying chemistry, or I can't even analyse anything, without understanding the atoms in reality. I believe in (Russell's??)...

A check my work question... Homework Statement Louis de Broglie tried to explain Bohr’s hydrogen atom electron orbits as being circles of just the right circumference such that an electron of the Bohr energy going around the circle will interfere constructively with itself. This seems to...

Problem A spin-1/2 is placed in a magnetic field with both x and z-components so that its Hamiltonian is H=-b_x \sigma^x-b_z\sigma^z, where \sigma^x and \sigma^z are the Pauli matrices. The real constants b_x and b_z have units of energy, and account for both the magnetic field components and...

A ket is expanded as \vert \nu \rangle = c_1\vert \nu_1\rangle+c_2\vert \nu_{2}\rangle . A measurement results in the eigenvalue a1. Is it possible to measure the other eigenvalue a2 at a time t after the first measurement? Could I write something like \vert \psi(t)\rangle = e^{-i \hat H t...

Hi guys, I consider the qm-derivation of the electronic states of hydrogen. There are two different derivations (I consider only the coulomb-force): 1) the proton is very heavy, so one can neglect the movement 2) the proton moves a little bit, so one uses the relative mass ##\mu## The...

Hi, I have been reading about quantum confined systems. That is, systems of 1 or 2 particles or atoms inside a region of space of radius R where potential energy is, say V(r), for r < R and infinity of r >= R. However, something I cannot find using Google is how one can obtain such space. I...

Now I am starting to learn Quantum Mechanics. In the class I am taught about operators, postulates and all other basic stuff. I understand operators to be +, -, /, etc; but quantum mechanical operators are entirely different; to understand them, I think, I need to know the historical...

Homework Statement The demonstration for the momentum operator in Quantum Mechanics goes something like this <v>=\frac{d}{dt}<x>=\frac{d}{dt} \int x \Psi^* \Psi dx and then one ends up with <p>=m<v>=\int \Psi^* (-i \hbar \frac{d}{dx}) Psi dx however, if you swap the congugates you get...

Hi All, I've heard it said that the superluminal phase velocity of the KG eqn is not a problem for relativistic causality because signals travel at the packet/group velocity, which is the inverse of the phase velocity (c being 1). I'm a bit skeptical of this. We can strip away all the quantum...

Homework Statement I've a physical system with ##l=1## and I have to calculate the values I can obtain if I measure ##L_x## and their probability.Homework Equations I know that: - the values I can obtain are ##\ m=0, \pm 1## - ##\displaystyle L_x=\frac{L_+ + L_-}{2}## - ##L_x|1, m>_x=\hbar m...

I think entanglement swapping shows the difference between measurement and observation. A measurement isn't as important as observation at least to subatomic particles. Here's some key points...

I've retired but have interests in Quantum mech. and Cosmology.

Hey guys, I really need your help. I have an exam tomorrow and no idea how to solve this task. Sorry for my bad english (did not use it for a long time). I hope that I translated the task correctly so that you might be able to help me. So We have two particles with spin=1 which means they have...

I know the debate about Schrodinger's cat is usually about things like consciousness but I want to talk about what it might say about isolated systems. Does the wave function of isolated systems remain in a superposition of observable states no matter how large the system gets? Say you have...

Hello,I'm new here and this is my first post. I am a freshman electronics and communication engineering student.I didn't study any quantum mechanics or solid state physics before(not in high school). But for my first year course i need to study solid state physics.The books we are suggested to...

This question, at the moment, is ridiculously difficult or even impossible to answer. Some prefer string theory, and some think that it is overly speculative and LQG may be a better fit, and some say the opposite. I would like to ask; In your opinion, what could be the right theory of quantum...

Suppose I am in a room and light(photons) from the light bulb reach my eyes, or I am outside light(photons) from the sun reach my eyes and I am able to see the objects around me. I want to know what factors affect the path of photons like temperature, gravity etc.I mean by knowing these factors...

How The physics of quantum Mechanics by James Binney compares to JJ Sakurai's Modern Quantum Mechanics? http://www.amazon.com/dp/0199688575/?tag=pfamazon01-20 http://www.amazon.com/dp/0201539292/?tag=pfamazon01-20 Which is more advanced?

I am confused by the my readings on the subject. Does superposition says that the system has all the values at the same time or it has one of the possible values but we don't know which one until "measured". And is there different answers for different observables. Moreover, how do these systems...

The Theoretical Minimum: Quantum Mechanics - https://www.amazon.com/dp/0465062903/?tag=pfamazon01-20 Sakurai Modern Quantum Mechanics - http://www.amazon.com/dp/0201539292/?tag=pfamazon01-20 I want to know, which book covers more in depth? And Sakurai's book is more advanced than Leonard...

In quantum mechanics, we can define the scattering amplitude f_k(\theta) for two particles as the coefficients of an outgoing spherical wave. More precisely, the asymptotic behaviour (when r\rightarrow\infty) of a wave function of two scattering particles, interacting with some short range...

I was looking at what Cohen-Tannudji has to say on compatibility of observables. Assumptions: ## A,B## are operators such that ##[A,B]=0 ## and we denote ## |a_i \,b_j\rangle## to be states for which ##A | a_i \, b_j \rangle= a_i | a_i \, b_j \rangle##, ##B | a_i \, b_j \rangle= b_j | a_i \...

So, I know that there are a lot of questions about good books on quantum mechanics and I have read each one of them, and I go on and bought Griffiths' Introduction to Quantum Mechanics. But the fact is that it did not build me a very good intuition as it emphasized the computational part of it...

I have studied physics during my undergraduate years but I want to relearn everything as I came to my realization that I'm weak because of the quality of education I got. So far, I want to know if my order of study is good. Classical Mechanics: An Introduction to Mechanics by Kleppner and...

Homework Statement The wavefunction ψ(x,t) obeys the time-dependent Schrodinger equation for a free particle of mass m moving in one dimension. Show that a second wavefunction φ(x,t) = ei(ax-bt)ψ(x-vt , t) obeys the same time dependent schrodinger equation, provided a = ħa2/2m and v = ħa/m...

Homework Statement Draw an energy level diagram for hydrogen (use the vertical direction for energy and separate the states horizontally by angular momentum l) Homework Equations I've got some fundamental misunderstandings with this one. I thought the energy levels of hydrogen were given by...

I mean the photoelectric effect of the hydrogen atom. It is weird. By the Fermi golden rule, the transition or absorption rate is proportional to the density of the final states. At threshold, the electron has zero momentum and thus zero density of state. Therefore, the absorption coefficient...

For a system consisting of multiple components, say, a spin chain consisting ofN≥3spins, people sometimes use the so-called geometric measure of entanglement. It is related to the inner product between the wave function and a simple tensor product wave function. But it seems that none used this...

Hello science buddies, This is my first post in this forum. Ok let me get to the point directly, currently I self-study graduate level quantum theory and the main book I'm using is Sakurai's. But I think for self studying it's better to also have a look at lecture notes, first because it's much...

I have not read any other QM books,i have little knowledge on that subject and want a books that uses mathematics in academic levels but is easy to get the grips on and also builds intuition and explains the phenomenons in a good manner.I do not want a book that emphasizes on mathematics or...

Not sure whether to post this here or in QM: I trying to numerically solve the Schrödinger equation for the Woods-Saxon Potential and find the energy eigenvalues and eigenfucnctions but I am confused about how exactly the eigenvalues come about. I've solved some differential equations in the...

why the solution for energy levels of electron in 1D crystal lattice as solved in Kronig penny model has used wave vector k differently then the Schrödinger equation solved for a free particle. (only the conditions in the equation has changed not the maths...so the "USE" of wavevector 'k' must...

As I undersand it, if you make a measurement on particle and get some observable property like spin, you can quickly make a second measurement and get the same outcome. How long do you have to make that second measurement before it starts evolving according to Schrodinger's equation and you...

i go to school, and it's quite far away (3 hours per day, return), so, i'd like to use this time wisely and learn QM, but unfortunately, i can't read books on transportation, i get dizzy... when i read things for prolong period of time.. i've only learned about the special relativity, and am...

i might have been spelling them wrong, but i can't find what do they mean: what's the difference between [psi](x) and [psi tilda](x)? i mean this thingy.. (~) and what's h(bar)? (in the formula p=h(bar)k) [i mean the bar thing] and other stuff.. things that i need to know...? i'm new to the...

So if we "look" at a particle, then its wave function collapses. Does "look" mean, hitting that particle with another particle (a light particle?). A simple Yes/No answers first please. I mean, does its wave function collapse because we first need to hit that particle with an electron or a...

... and its classical wave equation? Suppose in our double sit experimental setup with the usual notion of d,D we have a light of known frequency (v) and wavelength (L)- so its y=Asin(kx-wt). It passes through the two hole and move ahead doing the usual interference stuff, so final wave equation...

QM students study the singlet state, (|u>-|d>)/SQRT(2). Particles in the singlet state can be separated by any distance, and remain in the singlet state. That leads to the EPR paradox, Bell's Theorem and the more. My question has more to do with entering the singlet state. Leonard Susskind...

Hello, I recently read that MIT redesigned its EECS program. It redesigned it about 30 years ago to include more mathematics and solid-state physics but this time they are adding more QM. At my university, we study basic QM in freshman year physics and then again in third year in an EE subject...

Homework Statement Picture of Problem: Homework Equations $$\psi(x) = A_n e^{ikx} + B_n e^{-ikx}$$ for n=1,2,3 The Attempt at a Solution I know i need to relate the wave functions $$A_n e^{ikx} + B_n e^{-ikx}$$ for n=1,2,3 (the three areas of the barrier - before barrier, inside barrier...

I've taken a course in QM 1, based on the Schrodinger picture and QM 2 looks to be a continuation of this picture. Looking through Wikipedia, I found the article on the Dirac picture. Is there a good undergraduate (at the level of Griffiths or Shankar) textbook on this picture of QM? Since...

Homework Statement I would appreciate feedback on the following two problems: (1) For a given operator A with no explicit time dependence I am asked to show that d/dt(eAt)=A(eAt) (2) A free wave packet of width Δx is traveling at a constant velocity v0=p0/m. I am asked to estimate the...

I was wondering if the run away gravity in a super massive black hole could cause a lock up of sorts, and stop (nearly) all atomic movement? Packing the matter at it's core so tightly, that it would paralyze it at an atomic level. Could this possibly mean that near the center of these monsters...

Homework Statement You have a potential well, it's 1-dimensional and has a width of 0 to a. All of a sudden the wall of the well is pushed inward so that it's half as wide. Now the well is only extending from 0 to a/2. in the well is a particle (mass m) that is in the first excited state...