Schrodinger equation Definition and 549 Threads

is schrodinger equation capable of explaining all the properties of electron dynamics or are there any anomaly..? THANKS IN ADVANCE

hi all please help me... I'm learning schrodinger equation of a particle in a 1-dimensional box. I read a quantum mechanics book written by A. C Phillips. the wavefuction is ψ (x,t)= N sin (kx) e-iEt/hbar but when I compared to what I read from a modern physics book written by Beisser. the...

Homework Statement the question as well as the hint is shown in the 3 attachments Homework Equations The Attempt at a Solution i know how to normalize an equation, however i do not understand what the hint is saying, or how to do these integrals, any guidance would be greatly...

Homework Statement Consider the infinite well, a particle with mass m in the potential V(x) = \begin{cases} 0, & 0 < x < a,\\ \infty, & \text{otherwise,} \end{cases}, At t = 0 the particle is in the state: \Psi(x,0) = B \left[\sin{\left(\frac{l \pi}{a}x\right)} +...

Hello, I can't seem to find a reference formulating the Schrödinger equation as a set of two differential equations in terms of the modulus |\psi| and the phase S instead as one diff. eq. in terms of the complex wavefunction \psi = |\psi|e^{i S}. Can anyone show me the way?

I have the following Schrodinger equation: i* (h-bar) * partial derivative of ψ(x,t) w.r.t time = [(m*w^2 / 2) * x^2 * ψ(x,t) ] - (1/2m) * (h-bar)^2 * (laplacian of ψ(x,t))] m>0 is the mass w is a positive constant Assume that the ground state...

Greetings everyone, I haven’t done any quantum in a while, and was reviewing my textbook, Griffiths Ed. 1. The form of the Schrodinger equation I’m using is: i\hbar\partial\Psi/\partialt = -\hbar2/2m * \partial2\Psi/\partialx2 + V\Psi The book says if V is a function of x only, then the...

not all functions are wavefunctions. For functions to be wavefunctions they have to obey a series of "rules". Now, my question is: there are many functions, which obey these rules which aren't eigenfunctions of the hamiltonian, thereby meaning that they don't obey the Schrodinger Equation...

Suppose you've got a function \psi(t) that satisfies i\dot \psi = H \psi for some self-adjoint Hamiltonian H. I'd like to apply the fundamental theorem of calculus to this guy and write something like \psi(t) - \psi(0) = \int_0^t \psi'(s)ds. Can I do this, given only the very bare...

I'm an A-level student (I don't know what the US equivalent is sorry, I'm not an undergraduate is what I'm saying), and I've independently done a project on wave functions for a few simple stationary systems; particle in a box and quantum harmonic oscillator are the ones I focused on in the end...

This is a pretty trivial question, but how is the Schrodinger equation written out in full, time dependency and all in Dirac notation? I'm interested in this from a purely aesthetic point of view but I'm also a bit confused as to what the bras and the kets really are.

Homework Statement Given a wire with length a and square base b x b (where a >> b), show that the first 1700 (approximately) levels of the electron in the wire are identical for the one dimensional box, when a = 1m and b = 1mm. Homework Equations I know that the allowed energies of...

Hi, i am beginning elementary Quantum Mechanics as my course. While studying one question arise in my mind : In the solution of Schrodinger wave equation there are two parts. ψ=A*exp(jKx) + B*exp(-jkx). (for confined electron) But when dealing with free electron the solution is of...

Homework Statement In David Griffiths Introduction to Quantum Mechanics (2nd ed.), page 32 he normalizes a time independent wave function to get the coefficient A. He dropped the sine part of the integration with no explanation. What is the justification. Homework Equations The time...

Homework Statement Show that function Y = C sin θ (5cos2θ - 1 )ei\phi satisfies Scrhödinger equation for hydrogen? Homework Equations The Attempt at a Solution I derivated the required elements of the equation but ended up to some messy equation with lots of sines and...

Hi, Note: I will be sloppy with constant factors in this post. Only the general structure of the equations matters. Consider a particle in a linear potential, \frac{\mathrm d^2}{\mathrm d x^2} \psi(x) + x \psi(x) - E \psi(x) = 0. Mathematically, this is a second-order ODE, and there...

I have been trying to find an analytic solution to the time-dependent Schrodinger Equation. I plan to make a movie of the probability function as it changes over time, but I can't seem to find any analytic solution for the wave function. Is it possible to solve the time-dependent Schrodinger...

Homework Statement The solution of the Schrodinger equation for atom depends on four quantum numbers: the principal n, the orbital l, magnetic m1, and the spin Ms n = 1, 2, 3, 4, ... (integers) l = 0, 1, 2, ... (n-1) m1 = -1, -1+1,...0...1-1, 1 Ms = -1/2, 1/2 List all possible values of...

I discovered physics at a later age and am trying to learn more about Schrodinger's equation, here it is in one dimension -- got to crawl before you walk, I guess -- http://scienceworld.wolfram.com/physics/SchroedingerEquation.html == my question is the variable that is multiplied by i x h bar...

hi i need the schrödinger equation for a particle(electron) in a ring under the influence of a magnetic field that goes through perpendicular to the plane of the ring and i want to consider the spin too. Well, the particle in the ring is pretty easy: - \frac{ \hbar^2}{2mr^2}...

The postulates of quantum mechanics include: (1) Schrodinger's equation describes how the wave function of a system changes over time, and appears to make the wave function continuous over time. (2) When a measurement is made of quantity m, the wave function instantly changes to an...

Homework Statement A particle of mass m is confined in a two-dimensions by the potential energy V = 1/2k(x2+4y2). Write down the Schrodinger equation for the system. Write down the ground state wave function and find the lowest four energy levels in terms of the quantities ħ, k, m etc. Make...

ψ and its derivatives occur only linearly in the Schrodinger equation, that is, second or higher powers of these quantities do not appear in the equation. Schrodinger equation for a free particle is i\hbar∂ψ(x,t)/∂t = (-\hbar2/2m)(∂2ψ(x,t)/∂x2) Here (∂2ψ(x,t)/∂x2) is second power of ψ. Then...

Homework Statement Hello! I'm looking at a situation where there is a finite potential Vo for x<0, but zero potential for x>0. For a particle moving from left to right, I'm wondering what coefficients for the solution to the Schrodinger equation are equal to zero, and also how to prove that...

Homework Statement We have been examining a one-dimensional infinite square well where the infinite walls are located at -b and +b. The energy levels in this quantum system are non-degenerate, that is for each energy there is only one wave function. Let us place an infinite potential step...

hi i was currently thinking about this step here: \langle \psi_n, - \Delta \psi_n \rangle = \int |\nabla \psi_n|^2 dx how do you get from the laplacian to this other expression?

Why is it that we assume that the solutions to the time-independent Schrodinger Equation are real? Why can't they be complex?

In quantum mechanics, time independent Schrodinger equation gives dynamics of system. How do one claim that this equation is evolution of a system? Since dynamics need time dependency. How do one explain this discrepancy? Thanks in well advance...

In quantum mechanics, time independent Schrodinger equation gives dynamics of system. How do one claim that this equation is evolution of a system? Since dynamics need time dependency. How do one explain this discrepancy? Thanks in well advance...

Hi, could someone please explain the equation to me (its significance, application and the how the equation itself works) in simple terms? I find most other resources too complex for me to digest. I hope this is not too much to ask.

The Schrodinger equation for the complex conjugate of a ket vector is: d/dt<sai(t)| = -(<sai(t)|H)/(i*hcross) How do you derive the above equation from the normal form of the schrodinger equation? I'm mostly confused by where the negative sign is coming from. Thanks

Homework Statement See attached photo The Attempt at a Solution So I have no idea if I have even started this problem correctly so any help would be nice. My working is set out in one of the pictures. Any help would be appreciated I really am not quite sure what to do. Can't...

Hello, i am working on pulse propagation in optical fiber. i have to simulate the nonlinear Schrodinger equation using the FDTD (Finite Difference Time Domain) method. The Schrodinger equation has the form dA/dz = i/2 β2 d2A/dt2 –α/2 +iγ |A2|A where β2 is dispersion, α is...

Homework Statement See attached photo Homework Equations none The Attempt at a Solution Just hoping someone could give me a hand with this. I think I need to convert polar coords into y and z using trig then perform an addition of the wavefunctions as the linear transform...

Homework Statement Consider two non-identical, non-interacting particles of mass M that are constrained to move on a circle of radius R. Write down the Schrodinger equation for this problem and find the eigenfunctions and energy levels of this system. Homework Equations (see below)...

I understand that the Schrodinger equation describes the behaviour of matter and the electromagnetic wave down to the microscopic scale. But I'm not sure about the everyday sound waves, water waves, wave on a spring, etc. What do you think?

To what extent does the Schrodinger equation apply to an atom as a whole?

The Schrodinger equation is linear in time. I was wondering if that means that is not invariant under time reversal. That would be a surprise because all other microscopic laws (Maxwell's equations, Newton's equations) are time invariant. Can you please clear this doubt?

I've tried to solve Schrodinger equation for Charmonium and Bottomonium and there are some problems with that : 1. As we know the Schrodinger equation is independent from quantum number "ml" so there would be same Energy for different "ml" for a specific n. But what we see in PDG book is...

Why is the TDSE first derivative in time. Now I know that it is required so that the wave functions are complex... but is there any physical interpretation for this requirment??

Hi there, during my work on my PhD thesis as an experimental physicist I ended up with a very theoretical problem: What does the wavefunction of an electron traveling through a magnetic vector potential look like? I chose a cylindrical coordinate system with a magnetic vector potential A...

Schrodinger Equation in momentum space? ?? I don't know if this makes any sense at all, but I'm studying QM and just trying to generalize some things I'm learning. Please let me know where I go wrong.. Basically by my understanding the most general form of the Schrodinger Equation can be...

In standard, run-of-the-mill, one-dimensional scattering problems (e.g., finite square wells), we calculate transmission and reflection amplitudes by (in part) making sure that our wave function \psi satisfies the following conditions at discontinuities of the potential: (1) It is continuous...

I tried simply substituting z and epsilon into the original equation. I managed to get the second term of the left hand side correct but not the first term as I don't know how to turn z into d^2/dz^2. Can you please give me suggestions as to how I can approach this question. Thanks

From what I see, the time dependence in potentials do not change the spatial aspect of the wave function. They contribute a time dependence to the population of what were originally stationary states. If this is the case, then does that imply that the time independent bases are the ones we...

hi, can anybody of you show me how the schrödinger equation with the spin term of the electron for the hydrogen atom looks like? i really do not know how to do this Gavroy

Homework Statement Given a set of solutions |psi_n> to the TISE show that a) |Capital-psi>=Sum(C_n|psi_n>) is not a solution to the TISE Homework Equations ***H|psi_n>=E_n|psi_n> The Attempt at a Solution I don't really know where to start, I plugged |psi_n> into *** and I am...

Pardon my ignorance but why does the Time Independent Schrödinger equation use Time? It uses a kinetic energy operator. Kinetic energy; "It is defined as the work needed to accelerate a body of a given mass from rest to its stated velocity." Velocity is; "The scalar absolute value...

This extract is from my college notes. "Because of the inherent difficulty of obtaining even grossly approximate solutions of the complete Schrodinger equation, one typically focuses on reduced formulations that are believed to capture the essential features of the problem of interest. This...

Homework Statement Show that, if psi1 and psi2 are both solutions of the time-dependent Schr¨odinger equation, so is c(subscipt1) psi1 + c(subscript2) psi2 (where c1 and c2 are arbitrary constants). Homework Equations The Attempt at a Solution every source I've consulted so far...