Quantum mechanics Definition and 994 Threads

Hi all, I am reading the book "Emperor's New Mind" and have a question related to time asymmetry in state vector reduction (p.458) in quantum mechanics. Consider the following situation, as presented in the book: Suppose I have closed room with a lamp L, which emits light in some fixed...

I am an undergraduate physics major and I am taking a course on Big Data analytics. For the semester project, our professor has asked up to take up any field that interest us and do a project in that. I want to do something related to quantum mechanics or particle physics. Is that possible at my...

Homework Statement What is the best way to evaluate the rotation of a angular momentum eigenket (## | l,m \rangle ##) around an Cartesian axis? 2. The attempt at a solution I've tried to use the method in...

Homework Statement A cart roles down the track with an initial velocity vo. Because of falling rain, water starts filling the cart such that its mass increases linearly with time. The rain that has fallen on the track cause the wagon to experience a frictional force characterized with a...

Homework Statement a particle of mass m moves in 1D potential V(x),which vanishes at infinity. Ground state eigenfunction is ψ(x) = A sech(λx), A and λ are constants. find the ground state energy eigenvalue of this system. ans: -ħ^2*λ^2/2m Homework Equations <H> =E, H = Hamiltonian. p=...

Homework Statement Consider hermitian matrices M1, M2, M3, M4 that obey the property Mi Mj + Mj Mi = 2δij I where I is the identity matrix and i,j=1,2,3,4 a) Show that the eigenvalues of Mi=+/- 1 (Hint: Go to the eigenbasis of Mi and use the equation for i=j) b) By considering the relation Mi...

Homework Statement A function of a hermitian operator H can be written as f(H)=Σ (H)n with n=0 to n=∞. When is (1-H)-1 defined? Homework Equations (1-x)-1 = Σ(-x)n= 1-x+x2-x3+... The Attempt at a Solution (1-H)-1 converges if each element of H converges in this series, that is (1-hi)-1...

I'm attempting to learn the mathematics of quantum mechanics using textbooks such as "The Principles of Quantum Mechanics" by Dirac. I'm uncertain however of how ket vectors work! Say |A> + |B> = |C>, then what does |C> please represent?

Is there an easy explanation of total internal reflection of light using Quantum mechanics(or QED)?

Homework Statement Maybe I missed it, but in my notes and also in documents like (http://ocw.mit.edu/courses/physics/8-05-quantum-physics-ii-fall-2013/lecture-notes/MIT8_05F13_Chap_09.pdf) (equation 1.64), I see $$ \vec{r}\cdot\vec{p} = -i\hbar r \frac{\partial}{\partial r} $$ Where ##r## is...

Homework Statement At t=0 the wave function of a two-dimensional isotropic harmonic oscilator is ψ(x,y,0)=A(4α^2 x^2+2αy+4α^2 xy-2) e^((-α^2 x^2)/2) e^((-α^2 y^2)/2) where A its the normalization constant In which instant. Wich values of total energy can we find and which probability...

Hello everyone, In case of hydrogen atom, when we say spin up or spin down we refer to the z component of the spin. Why are we interested only in the z component of spin and not in the x and y components? Thanks in advance

Did string theory come about as a possible solution to quantum mechanic's "something being in several places at the same time" paradox so to speak? I am not a math-guy or pretend to know anything about physics. I m just curious. I was thinking that what appears as something being in multiple...

I am a beginner in quantum mechanics and I am confused about the operator ΔA defined to be ΔA Ξ A - <A>. Can someone please tell me how to interpret <A>? From what I can understand, <A> is the expectation value and is defined to be <Ψ|A|Ψ>. But that is just a scalar correct? How do subtract a...

Homework Statement Like ordinary wave, a particle’s wave function can be described as countless line of sine wave’s superposition. However it can also be clarified as vibration (the complex amplitude still follow the rule of local conservation) I think these two explanation are equal. Am I...

Hi, I am looking for textbooks in relativistic quantum mechanics and group theory. I have just finished my undergraduate studies in Physics and am looking to specialise in theoretical high-energy physics. Therefore, textbooks in relativistic quantum mechanics and group theory suited for that...

Hello all. I had some questions on some of the specifics of matter-antimatter annihilation. I've tried looking this up but haven't had much success. If you guys know of any textbooks or journal articles that dig deep into the mechanics I'd be grateful if you'd post them. Anyway, my basic...

before measuring an electrons position, is it physically a smear,like a wave? Or is it just nothing?

Homework Statement Linearly polarized light of wavelength 5890 A is incident normally on a birefringent crystal that has its optic axis parallel to the face of the crystal, along the x axis. If the incident light is polarized at an angle of 45° to the x and y axes, what is the probability that...

In interpretations where the wave function is real, what does that mean? does it mean that the wave function has physical meaning?

I completely have no idea what time-reversal mean. Why does, by substituting -t into an equation and if the result is the same as the original equation, then the equation is said to be time-reversal symmetry? Also, what does that 'symmetry' mean there? An even function?

If I have a wave function given to me in momentum space, bounded by constants, and I have to find the wave function in position space, when taking the Fourier transform, what will be my bounds in position space?

I have been recently introduced to QM and I am deeply interested in it. I have come to know that quantum cryptography, quantum computing, and quantum optics are the hot areas where research is going on. But I'm curious, is there theoretical research going on for understanding of the quantum...

Dear Physics Forum friends, I am a college undergraduate in US with double majors in the mathematics and computer science. I have been doing research in the theoretical computer science, and I recently got interested in the quantum cryptography. Since I cannot take any physics course until...

Can the general solution to the Schrodinger equation be asymmetric (has neither even or odd solutions)? Question (1): I saw somewhere that you cannot have a solution that is both-- it must be either odd or even, and I was wondering: why? I was working on a problem where the potential function...

Homework Statement My teacher made up this question, but I think there's something wrong. Consider the wave packet in momentum representation defined by Φ(p)=N if -P/2<p<P/2 and Φ(p)=0 at any other point. Determine Ψ(x) and uncertainties Δp and Δx. Homework Equations Fourier trick and...

Homework Statement Show that the maximum of the Planck energy density occurs for a wavelength of the form λmax = b/T, where T is the temperature and b is a constant that needs to be estimated. Homework Equations Planck energy density u (v,T) = 8πv2 / c3 * hv / ehv/kT-1 The Attempt at a...

Homework Statement A particle is described by the state of the following wave function. wavefunction(x,y) = 30/[(a^5)(b^5)]^1/2 * x(a-x) * b(b-y) Homework Equations integral from 0 to i of x^n * (1-x)^m dx = (n!m!)/(n+m+1)! The Attempt at a Solution I know that normalizing means taking the...

Hello everyone! I'm trying to follow a solution to a problem from the book "Problems and Solutions on Quantum Mechanics", it's problem 1017. There's a step where they go on too fast, and I can't follow. I've posted the solution and where my problem is down below. Homework Statement The dynamics...

My question stems from a discussion I had with my colleague today. In Electomagnetic coupling , like in waveguide structures. We apply pertubation theory to find out the coupling between various modes that get coupled in the device. My colleague said that the coupling interaction was...

I've just recently learned about Yves Clouder's hydrodynamics models that show quantum mechanics behaviour emerging from a vibrating fluid. As a "born-again student", this seems very exciting to me - especially in the sense that at the very least it offers a mental model that helps come to grips...

I have heard that in my next semester, our quantum mechanics teacher will be giving a great emphasis on difficult integrals with the most of them having to do with gamma functions. Does anybody know a book(or any other source) that I can learn about and practice gamma functions integration...

Hello everyone! I would like you to recommend me a book for relativistic quantum mechanics. It's for an undergraduated class. thanks

Being a non- physicist, it is extremely difficult for me to conceptualize QM. I hope to get some definite help at this forum. QM says that the sub-atomic particles exist as both waves and particles. It is not that much difficult to conceptualize. QM also says that the sub-atomic particles can...

Derive the probability current density for a particle in an electromagnetic field. (I previously posted this on StackExchange. Please pardon, but I have been spending a lot of time on this and if anyone knows exactly what the subtle trick involved is, I would really appreciate it.)...

Homework Statement Two particles, their spin are 1/2. The hamiltonian is ##H=\gamma s_1 \cdot s_2## At t=0, the state ##|\alpha(0)>## is such as ##s_{1z}|\alpha(0)>=\hbar/2 |\alpha(0)>## and ##s_{2z}|\alpha(0)>=\hbar/2 |\alpha(0)>##. Find the state ##|\alpha(0)>##.2. The attempt at a...

Homework Statement Suppose a linear operator L satisfies <A|L|A> = 0 for every state A. Show that then all matrix elements <B|L|A> = 0, and hence L = 0. Homework Equations ##<A|L|A>=L_{AA} and <B|L|A>=L_{BA}## The Attempt at a Solution It seems very straight forward and I don't know how...

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...

It's been a little bit since I have studied multi-particle quantum mechanics and I am a little rusty on the notation. Let's say I have a wave function, that consists of the tensor product of two spaces, one for each particle moving, ##|\psi_1,\psi_2>##. Each of these particles is moving in a...

http://www.pnas.org/content/109/24/9314.full According to the experimenters they have found out which path the photon took and still observed the interference pattern. So they know that the particle went through the left or right slit but at the same time saw the interference pattern built up...

Hi there. I had this question going around in my mind for a long time. Basically, I wanted to know if there is a need for the use of the complex field for the wave functions in quantum mechanics, or if quantum mechanics can be built with real wave functions, instead of working in the complex...

Hey! I was working with Dirac's equation: $$ ( i \hbar \gamma^\mu \partial_\mu - m ) \psi = 0, $$ and I found that if you work with a function that depends on the momentum, $$ \psi ( \mathbf{p} ), $$ you obtain: $$ ( i \gamma \cdot \mathbf{p} + m ) \psi ( \mathbf{p} ) = 0. $$ The problem is...

Hi, I am a math major, currently in my 3rd year of undergraduate studies, majoring in measure theory / probability / mathematical statistics. I am in the dubious situation that I will be taking a course on QM while having so far only studied classical mechanics (i.e. all chapters on classical...

1. Homework Statement p: momentum x: position t: time h_bar: Planck's constant Ψ: wave function Homework Equations The Attempt at a Solution I've posted a link to pictures. http://imgur.com/a/TKvUu I'm not vera good at using LaTex yet :( So I've shown that the wave equation satisfied the...

In 2012, experimenters showed that when two entangled photons separate and when one goes through the double slit, we can tell which slit it went through and see that they still created an interference pattern because the photon that it was entangled to tells us which slit it went through. What...

In the double slit experiment, what is the position and momentum of an electron/photon? Is the position of the electron/photon which slit it went through? And is the momentum of the electron/photon the wave like interference pattern detected on the detector screen?

Homework Statement I Have tried to solve a problem about infinite potential well with a delta well in the middle, but I haven't the results and so I can't check if the proceeding is wrong. I post the steps that I have followed hoping someone can help me to understand. We have a particle in 1D...

Hello everyone! I just finished studying basic quantum mechanics, using Liboff's "Introductory Quantum Mechanics", i.e. wavefunctions, uncertainty relations, basic 1D problems, dirac notation, angular momentum (orbital and spin, addition, eigenfunctions, Clebsch-Gordan coefficients etc)...

Homework Statement I'm trying to understand how we can find - at the first order - the energy-shift and the eigenstates in a degenerate case. My notes aren't clear, so I have searched in the Sakurai, but the notation is different, I have read other notes but their notation is different...

Hallo everyone! I am studying Physics at University level. This Fall I will enter the third year of my studies. I find the curriculum inadequate and thus try to learn stuff on my own. I have already taken the basic courses in Calculus (single and multivariable), Complex Analysis (analytic...