In quantum mechanics Definition and 251 Threads

There are many n's in QM, and I am confused as to which is which. For example, there are: n called principal quantum number n_r=n-l-1 (anonymous n) n_i in E=({3\over2}+n_x+n_y+n_z) and n=\sum_i n_i n the indices of energy as in E_n and lots more Could anyone kindly help me...

Can anyone explain to me what Degeneracy is properly. I know its something to do with having different eigenvalues on the same energy level or something like that, but have not been able to find a good explanation in any textbooks or anywhere online. And how does something have infinite...

Homework Statement i know that H |n> = \varepsilon_n |n> H |i> = \varepsilon_i |i> and i want to estimate < n | e^{i H t / \hbar} V(t) e^{-i H t / \hbar} |i> Homework Equations <\psi | \varphi> = \int \psi^*(q) \varphi(q) dq The Attempt at a Solution i don't understand well how the...

Hi- I recently read Brian Greene's Fabric of the Cosmos which led me to think of an interesting concept that I would appreciate further explanation on. On page 456 Greene describes how in the multiverse view, if you traveled back to the past, you would have gone back to a past in a parallel...

Maxwell equations are based on the wave nature of electromagnetism so they can't explain why the electron revolving in Bohr's orbit does not emit radiations.So my question is can't the Maxwell equations be modified according to the particle nature(quanta) of electromagnetism

Can someone please elaborate these lines: "Causality applies only to a system which is left undisturbed. If a system is small, we cannot observe it without producing a serious disturbance and hence we cannot expect to find any causal connexion between the results of our observations. "...

The problem is very easy, maybe just something about eigenvectors that I'm missing. Go to the first two pages of the 5th chapter of ''Principles of Quantum Mechanics'', by Shankar, 2nd edition. Homework Statement Shankar wants to find the solution for a free particle in Quantum Mechanics...

I have a question regarding the variational principle in quantum mechanics. Usually we have a Hamiltonian H and we construct a state |ψ> using some trial states. Then we minimize E = <ψ|H|ψ> and get an upper bound for the ground state energy. In many cases the state |ψ> is then used to...

How do mirrors work in quantum mechanics? Does light get absorbed by the atoms and then emitted at the same frequency? Or is something else going on?

Homework Statement There is a combined system with angular momenta j_{1}=\frac{1}{2}, j_{2}=\frac{3}{2} and j_{3}=1. The Hamiltonian of the composite system depends only on the total angular momentum. What are the states of the combined system? What are the degeneracies of the eigenenergies...

I'm almost finished with his book finding darwin's god. In short, I feel like he skirts dangerously close to ID with this notion. Basically, Miller reconciles evolution with God by saying that, while this could be reductionist, it was God that created the conditions that led rise to...

Does a particle's diameter affect anything in determining its position, momentum, energy, etc.? Does it play any role in Shrodinger's equation?

Homework Statement This is more maths than QM I think, but it's at the beginning of my Quantum Questions. Basically, it's about rotations preserving length: [FONT="Times New Roman"]xi is the ith component of a vector, and the length of a vector is determined by the metric ηij...

Studying a maths degree, going onto final year next year, am planning to do a 3rd year course in quantum mechanics. I just want to ask, how much probability theory and differential equations are there in quantum mechanics? Someone said that ultimately quantum mechanics is about probability...

Not every state can be represented by a direct product. Do states that can be written as a direct product have anything special about them? It seems that states that can be written as a direct product lose correlation between between each individual state. More specifically, stronger than...

I am just wondering what stage are we at in Quantum mechanics relative to Newtonian mechanics? I think we are well sorted with the latter but is ourknowledge nowadays of QM equivalent to the egyptians thinking the sun was god thousands of years ago? Shouldnt we start working on theories...

Homework Statement Suppose you have a particle in a box of length L (a cube). Suppose a particle is in a given state specified by three integers n1,n2,n3. By considering how this state must change when the length of the cube is changed in one direction, show that the force exerted by the...

Please teach me this: Why the motion equation must be:dA/dt=[H,A] where H-Hamintonian,A-operator of any observation,because with a local flow t(time) of vector X in a manifold we can write the Lie derivative:dA/dt=[X,A].(Where we consider time t as one-parameter group and as local flow of some...

Can you please tell me were I am wrong? I define the entropy (as usual) as S[\rho] = -k_B \text{tr}(\rho\ln\rho) The time development of the density operator is \rho(t) = U(t)\rho(0) U^\dagger(t) That means S[\rho(t)] = S[U(t)\rho(0) U^\dagger(t)] = S[\rho(0)] where I used...

I am not a physicist, so please excuse the gaps in my knowledge. I am writing a would-be philosophical essay about models in different fields of research. In most general terms, my task is to consider how modelling can be useful in the pursuit of knowledge in the widest understanding of the...

I have been doing some research on Leonard Susskind and how he claims information is conserved. I don't think if we reverse time we will get back what we started EVERY single time. Thinking that information is conserved really doesn't make sense to me. What do you think? If you agree with me...

I'm unsure about how parity is used or indeed what it actually is in quantum mechanics. If someone could shed some light on this it'd be a great help.

Do golden ratios appear in quantum mechanics - such as with the standard model, string theory or quantum gravity?

In classical mech, we heard of force, but in quantum there is no force mentioned at all. why? I am rather puzzle by this fact.

I have nothing to add to the question that opens this post.

Homework Statement Hi Please take a look at the following equality found in my book: \left| \mu \right\rangle = \sum\limits_v {\left| v \right\rangle \left\langle {v} \mathrel{\left | {\vphantom {v \mu }} \right. \kern-\nulldelimiterspace} {\mu } \right\rangle } =...

Homework Statement H=(J1^2+J2^2)2A+J3^2/2B where J1,2,3 are the angular momentum operators and A and B are just numbers Homework Equations The Attempt at a Solution I rewrote the Hamiltonian as (J^2-Jz^2)/2A + J3^2/2B and got the eigenvalues to be (h^2L(l+1)-h^2m^2)/2A+h^2m^2/2B...

Homework Statement 1. Is state \psi_{0,2,1}-\psi_{5,0,1} an eigenstate of L_{x} 2. Is state \psi_{1,3,1}-\psi_{4,2,0} an eigenstate of L^{2} Homework Equations Stationary state of Hamiltonian defined by: [itex]\psi_{n,l,m}[/tex] where the subscripts denote quantum numbers. The...

hi, which phenomena is known in quantum mechanics to cause a negative pressure? as far as I know, the vacuum energy of the time energy uncertainty has a very low energy density but it should have a positive pressure because it pushes and not pulls, am i right? so which phenomena actually...

Homework Statement Find the operator for position x if the operator for momentum p is taken to be \left(\hbar/2m\right)^{1/2}\left(A + B\right), with \left[A,B\right] = 1 and all other commutators zero. Homework Equations Canonical commutation relation \left [ \hat{ x }, \hat{ p } \right ] =...

Hello, suppose one has a classical canonical transformation between two sets of canonical variables such that the new (primed) positions and momenta can be written as functions of the old (unprimed) ones. {\cal K}: x_i \to x_i^\prime(x); \quad p_i \to p_i^\prime(p) Using these relations one...

I hear the term Wave used in extreme frequencies whenever Quantum Mechanics is discussed but I am not entirely sure what exactly is a wave. Can a wave be thought as a particle whose position is unspecified with multiple areas where it may impact the surface of another object. Or is a wave a...

Of course every prove of this type have some mistake. If nobody will see I will post solution! \hat{A}, \hat{B} - linear, hermitian operator which commutator is [\hat{A},\hat{B}]=i\hbar\hat{I} \hat{I} - unit operator Eigen problems of operators are: \hat{A}|\psi \rangle=a|\psi...

Apologies for any vagueness or ignorance here (and lack of citations) but I remember reading that ferromagnetism arises from spin behavior of many electrons. So in a broader sense, are all magnetic fields arising from spin? I am trying to understand how magnetic fields can be viewed at the...

I want to know what does velocity really mean in quantum mechanics. Since the particle doesn’t have exact position, how can we talk about the velocity and momentum?

How do we define veliocity of a particle in QM? How it's related to the momentum. Are there any ways to cimpute quickly mean value of veliocity.

I'm confused about choosing the value for energy in quantum mechanics problems such as in scattering, tunneling, boundstates.. problems because this affects later calculations. Given the potential in some regions, how do I decide energy to be negative or positive, or greater/less than the energy...

What is box normalizing and why is it important in quantum mechanical problems such as the black body radiation?

Are there any other good books such as LIM series which include solved problems on QM,Stat Mech & atomic physics ?

I read article http://arxiv.org/abs/quant-ph/0401170 It obtains how Dopler frequency change exponentialy with time for accelerated observer. Then it does Fourier's transformation of this waving and it gets thermical radiation. But, where in quantum mechanics it is supported that we make...

I haven't been studying quantum mechanics for very long, and I've only just started reading about the path integral formulation, so I don't know many of the details yet, but I noticed something peculiar. The path integral formulation is possible because of the similarities of the Schroedinger...

I seem to be missing the resources that describe how gravity is not found in quantum mechanics. What phenomena in quantum mechanics illustrate that gravity is [thus far] not a part of it? This is not a homework question. I know that gravity is incompatible with what we know about QM. What...

According to Heisenberg uncertainty principle, certain events such as double slit and decay of an atom has no causal history, hence a violation of causality, uncaused events. But relativity states faster than light travel violates causality. Since quantum mechanics does not respect...

Homework Statement The solution of Schrodinger’s equation for a free particle can be written in the form: \psi(x,t) = \frac{1}{\sqrt{2\pi}}\int_{-\infty}^{\infty}\phi(k)e^{i(kx-wt)}dk [Q1]: Explain why the function \phi(k) is given by: \phi(k) =...

We're working on the parity operator in my second semester quantum mechanics class and there is one point I am confused about, either in the definition of degeneracy or in the parity operator itself. We talked about a theorem whereby the parity operator and the Hamiltonian cannot share...

I am stuck at the problems of Boundary conditions for two dimensional problem in QM. iIf we have a two-dimensional domain, along the boundary, we can define two directions, one is tangential, the other is normal, assuming that there is no current flowing in and out along the normal direction...

What is exactly the creation and annihilation operator in quantum mechanics? What its physical significance?

Homework Statement A wave in quantum mechanics is represented by Aei(kx-\omegat). Show that a standing wave looks like 2iAe-i\omegatsin(kx) by subtracting two waves moving in opposite directions. (Hint: make the k negative in one of the waves) Homework Equations As far as I know, the 2...

Some things are statistically impossible in QM, I believe, but are things there physically impossible?

Homework Statement I am trying to derive a property of the Fourier Transform of the wave function. F[\psi(cx)]=\frac{1}{|c|}\overline{\psi}\left(\frac{p}{c}\right) Homework Equations The Fourier transform of \overline{\psi}(p) is defined as...