Schrodinger equation Definition and 549 Threads

Okay, so I'm actually an economics major but I LOVE physics; especially quantum physics. Unfortunately my knowledge of physics is limited only to the conceptual side of physics (something I'm working on changing). I spent a lot of time thinking of getting a tattoo I really wanted and settled on...

Homework Statement [2 Dimensional infinite square well] Show that you can separate variables such that the solution to the time independent schrodinger equation, ## \hat{H} \psi (x,y) = E \psi (x,y) ## can be written as a product state ## \psi (x,y) = \phi (x) \chi (y) ## where ## \phi (x)##...

There are few questions on an assignment (taken from an old exam, YIKES!) that are confounding me and I was wondering if you in the physics community could help. Here is the question; Given the wavefunction, ψ(x,t)=∫PHI(p)*exp[i((px-E(p)t)/hbar)]dp For the case where a quantum particle is...

Suppose I have a Schrodinger equation for two interacting particles located at x and y; so, something like \left( i \frac{\partial}{\partial t} + \frac{1}{2m_x} \frac{\partial^2}{\partial x^2} + \frac{1}{2m_y} \frac{\partial^2}{\partial y^2} + V(x-y) \right) \psi(x,y,t) = 0. Now, I want to...

A particle of mass m is in the state \Psi (x,t) = A e^{-a[(mx^2 / \hbar ) + it]}Find A For what potential energy function V(x) does \Psi satisfy the Schrodinger equation? Do I just re-arrange for A? (Sorry if I seem really dumb). I'm not really getting this.

Hello, this is my first thread here and i have a question regarding coherent population trapping and the dark state. I am from Germany, so please excuse me, when my english isn't very good. This is what I found on wikipedia: http://en.wikipedia.org/wiki/Dark_state in the section...

i think every system is accurately described by Schrodinger equation. so what is the point of using old quantum mechanics methods? with Schrodinger equation, at least numerically, you can solve the eigenvalues and eigenvectors readily and accurately. So what is the point of using...

How do we differentiate the solution of Schrodinger equation for closed and open system.

Homework Statement An ice-hockey puck has the weight 0.170 kg. The ice-hockey rink is 30x60 m. If no players are on the ice, what speed does the puck have due to the quantum effects (ground state)? Homework Equations The wave-equation solution to the Schrodinger equation is ψ(x,y) =...

Homework Statement The solution to the Schrodinger equation for a particular potential is psi = 0 for absolute x > a and psi = Asin(pi*x/a) for -a <= x <= a, where A and a are constants. In terms of a, what value of A is required to normalize psi? Homework Equations psi = 0 for absolute...

Homework Statement An eletron is moving along one axis between x=0 and x=L. It's mass is given by m. We want to know the energy and wave function of its possible states given by the quantic number n. Show that the solution to the above equation is En=n^2*h^2/(8*m*L^2)...

My chemistry teacher showed this slide but didn't explained how the marked step in the dedution of the schrodinger equation. Please help! I really don't know where I can find the answer, it's the first time I see the Schrodinger equation!

So I understand the schrodinger equation (independent), but I'm a kind of person who understands something better after an example or two, can someone help me and give me one for a H-atom or Hormonic Oscillator? Thanks, and sorry if this is the wrong place to put this post...

Everywhere I look,in every textbook,online texts,video tutorials,everywhere,Schrödinger equation is always solved via separating variables. I want to know is there a way to solve Schrödinger equation(of course I mean time-dependent Schrödinger equation)without separating variables? Is it...

I know that one solution to the Schrodinger equation is Aexp(i(kx - ωt)) Is there a special relationship between k and ω for this to be a solution, or is it always a solution?

Should the time independent Schrödinger equation contain a differentiating 'd' as shown here: http://vergil.chemistry.gatech.edu/notes/quantrev/node8.html or a differentiating curly 'δ' as shown here: http://hyperphysics.phy-astr.gsu.edu/hbase/quantum/scheq.html Thank you!

Homework Statement What is the probability that a particle in the ground state will be found between L/2 and 2L/3? im new guys so go easy :) Homework Equations ∫ψ(x)^2 dx = ∫2/L (sin(πx/L))^2 dx in attachment The Attempt at a Solution The answer should be 30.44% i got 66.66% and sometimes a...

Homework Statement Im reading and thinking about the interpretation about Schrödinger equation s solutions (wave functions) - what they really mean. What does the amplitude of wave function correspond to? Does it mean that if amplitude is greater then energy of particle is greater as well ...

I have seen its name in many articles I have read but I would like to know. What is it and what is its use?

Does the Schrödinger equation completely neglect the uncertainty principle? If so, wouldn't this imply that our intensity distribution has its own probability distribution?

When my book deals with bound states and scattering states it puts: E<0 bound state, E>0 scattering state. What reference for the potential have been used for these?

In clssical mechanics it doesn't really seem to matter which reference point you use for your potential. All that matters is the difference in potential between two points. Does the same hold true for the potential you plug into the Schrödinger equation? It doesn't seem so since plugging in...

Hi! I think this should be a fairly easy question to resolve, but it's currently giving me fits... Suppose we consider a system of three interacting particles where we assume two of the particle (at positions r1 and r2) have infinite mass (such that we can ignore their kinetic energy) and do...

Hello, In the book physical chemistry (P. Atkins & Julio de Paula, 2009, 5 ED) the authors derive a justification of the Schrödinger equation. 1.) \frac{-\hbar^{2}}{2m} \frac{d^{2}\psi}{dx^{2}}+V(x)\psi=E \psi The derivation goes as follows: Derivation: We can justify the form of...

Classically, particles seek configurations of least potential energy. Something like this happens in QM: the wavefunction will usually be densest in those areas the potential energy is smallest. But looking at the Schrodinger equation itself, I can't see intuitively why this should be.

Does it have an easy classification (elliptic, hyperbolic, parabolic, for example)? Or does the fact that it has an "i" in it make this impossible?

Homework Statement An electron is confined within a three-dimentional cubic region the size of an atom where L = 200 pm. a) write a wave equation for the electron b) wirte a general wave function for the possbile states of the electorn. List any quantum numbers and their possible values...

I have learned time-independent schrodinger equation only from my textbook. I know Eψ(x) = - hbar^2 / 2m ψ''(x) + Uψ(x) and ψ(x) = Asinkx + B coskx what if it's three dimention? do I do Eψ(x, y, z) = - hbar^2 / 2m ψ''(x, y, z) + Uψ(x, y, z) ? and what is the wave equation supposed to be?

Homework Statement Consider the one dimensional wave funciton give below. a) Draw a graph of the wave function for the region defined. b) Determine the value of the normalization constant c) what is the probability of finding the particle between x = 0 and x = a/2 d) show that the wave function...

Hello guys, in the attached file, I can't understand how the guy arrived to the equation in the red rectangle. My problem is: how could there not be dC2/dt term. Why only dC1/dt term? ψ contains both C1 and C2, and when the derivative is applied, both have to be influenced, and both are...

I'm reading the Wikipedia page for the Dirac equation I am not sure how one gets a new \rho and J^\mu. How does one do to derive these two? And can anyone show me why the expression for density not positive definite?

Homework Statement When solving, say, the double delta function potential well, we fix constants using continuity. If the potential is symmetrical about the origin, can we conclude that the wave function, i.e. the solution, will also be symmetric? I found this way made the calculations much...

Hello - A few questions I have after watching Brian Green’s The Elegant Universe – Within the video Dr. Green shows a neat way to view the different scales relativity and quantum mechanics are involved with. He takes an elevator to a top floor to show relativity’s applicable scale. He steps...

Schrodinger Equation, "Potential" This is a very simple question, but I am confused. I have seen Potential and Potential Energy interchanged.. yet still referred to as potential. Is the "potential" function in the schrodinger equation really a potential function or potential energy? (units...

Hi, I several times heard that one way to describe the collapse of the wave-function is to add non linearities in the Schrodinger equation (I know that this approaches are not convincing but that's not my point), however, I don't see why a non linear SE would imply loss of unitarity? As long...

So I've been trying to understand this equation for a long time, about half a year - I don't know someone who could teach me this either due to the fact that I am only 15 and going into my final year in secondary school after August and according to most colleges (UK college, not American) in my...

While I was studying Ch 2.5 of Sakurai, I have a question about Green's function in time dependent schrodinger equation. (Specifically, page 110~111 are relevant to my question) Eq (2.5.7) and Eq (2.5.12) of Sakurai say \psi(x'',t) = \int d^3x' K(x'',t;x',t_0)\psi(x',t_0) and...

I've been looking into the time independent schrodinger equation (E\Psi = Ĥ\Psi.) I know that \Psi is the wave function and Ĥ is the hamiltonian operator. I know that Ĥ is the total of all the energies in a system. What exactly is the wave function? Is it a quantum state? And what does the E...

If you've got, say, three particles, then the time-dependent Schrodinger equation (in units where \hbar = 1) for the system reads i \frac{\partial \psi}{\partial t} = -\sum_{i=1}^3 \frac{1}{2m_i} \Delta_i \psi + \sum_{i<j} V(r_i - r_j)\psi, right? And of course \psi = \psi(r_1,r_2,r_3;t)...

Hi, In Griffiths QM, it is claimed that to solve the Schrodinger Equation, we take the solution wavefunction \Psi(x,t) to be of a seperable form \psi(x)\phi(t). He then says that a superposition of these seperable forms can always give us the general solution. Can someone help me prove that...

Note : I am not sure this is the right section for posting it , but from the rules section i saw that this section can be used for homework related queries and independent study . Homework Statement Understanding schrodinger equation . i want to understand the solutions of this equation and...

The general evolution of a ket |\psi\rangle is according to -i\hbar\frac{d}{dt}|\psi\rangle=H|\psi\rangle without specifying a representation. From this equation, how can you simply get a equation in a certain representation F as below: -i\hbar\frac{\partial}{\partial t}\langle...

Hello, I'm reading Griffiths' introduction to elementary particles and he seems to claim that the Schrödinger equation can be seen as a non-relativistic limit of the Dirac equation. I was wondering how one could deduce this, e.g. how do we go from \mathcal L = \bar{\psi} \left( i \gamma^\mu...

Ok, I understand the schrodinger equation for the most part, the thing is though, I don't understand what ∂ means... In the equation:(∂^2ψ/∂x^2)+8(pi)m/h^2(E-V)ψ=0 It pops up two times. The rest of the equation is kinda self explanatory, but I don't know what on Earth ∂ means please, tell me...

The normalization condition is: ∫|ψ|^{2}d^{3}r=1 In spherical coordinates: d^{3}r=r^{2}sinθdrdθd\phi Separating variables: ∫|ψ|^{2}r^{2}sinθdrdθd\phi=∫|R|^{2}r^{2}dr∫|Y|^{2}sinθdθd\phi=1 The next step is the part I don't understand. It says: ∫^{∞}_{0}|R|^{2}r^{2}dr=1 and...

How can i solve Schrodinger equation in 3dimension i want to know how can i deduce every equation ? and how can i find equation of spherical harmonic and radial equation ? i need to understand this proof

At the moment I am studying the Schrodinger equation using this resource. In a 1D solution (sec 3.1 in the paper) they show that a wave function can be expressed as \Psi(x,t)=\sqrt{2}e^{-iE_{n_x}t}\sin (n_x\pi x) where n_x is the quantum number. And they show the real part of the solution in...

Why "i" in Schrodinger Equation Schrodinger Equation is "i*h*dphi/dt=H*phi" That is to say that the change in the state is proportional to a linear tranformation of the actual state (I understood the logic behind that), H is hermitian and that means that its eingenvalues are real (right?)...

Homework Statement Hello! I am currently stuck with a time independent Schrodinger equation where the potential "V(x)" is hyperbolic in nature. I was wondering if anyone could give me a hint as to how I should approach this problem in order to get an analytical solution (without using...

Hi, I'm doing a homework problem in my modern physics class and I'm stuck at a point. The question is "Show that the radial probability density of the 1s level in hydrogen has its maximum value at r = a0, where a0 is the Bohr radius" I know that the radial schrodinger equation will...