Schrödinger Definition and 591 Threads

The Schrödinger equation solved for the hydrogen atom gave good agreement with spectral lines, except for line doublets. To account for these electron spin theory was grafted onto the theory, despite the problem of electron being a point particle. In 1928 Dirac gives his different answer...

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 Schrödinger 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

Hi all, In class I've recently been taught the Schrödinger equation and about spin(couple weeks apart). My questions are- 1. In laymans terms, what exactly does the S-eqn mean? What I have taken it to be so far, is an equation that determines the probability of the position of an e- in...

Homework Statement Derive the Non-Linear Schrödinger from calculus of variationsHomework Equations Lagrangian Density \mathcal{L} = \text{Im}(u^*\partial_t u)+|\partial_x u|^2 -1/2|u|^4 The functional to be extreme: J = \int\limits_{t_1}^{t_2}\int\limits_{-\infty}^{\infty}\...

At the moment I am studying the Schrödinger 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...

Schrödinger and Infinite Square Well... hell Homework Statement Show that Schrödinger Equation: \frac{d^{2}\psi(x)}{dx^{2}}+k^{2}\psi(x)=0 has the solution \psi(x)=A\sin(kx) Homework Equations k=\frac{\sqrt{2mE_{tot}-E_{pot}}}{\hbar} The Attempt at a Solution I already know that...

Why "i" in Schrödinger Equation Schrödinger 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 By substituting the wave function \psi (x) = Ax{e^{ - bx}} into the Schoedinger equation for a 1-D atom, show that a solution can be obtained for b = 1/{a_0}, where {a_0} is the Bohr radius. Homework Equations - \frac{{{\hbar ^2}}}{{2m}}\frac{{{d^2}\psi...

Homework Statement Hello! I am currently stuck with a time independent Schrödinger 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 Schrödinger equation will...

is Schrödinger 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 Schrödinger 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)} +...

Consider the potential V(x) = \begin{cases} 0, & x < -a & (I) \\ +W, & -a < x < a & (II) \\ 0, & x > a & (III) \end{cases} for a particle coming in from the left (-\infty) with energy E (0 < E < W). Give the solution to the Schrödinger equation for I, II and III and use these to...

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 Schrödinger 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 Schrödinger 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 Schrödinger 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 Schrödinger 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.

hi , can anyone please explain to me what is wavefunction - and can we apply schordinger wsve equation to simple pendulum. thanks

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...

Homework Statement What are the similarities and differences between the quantization of angular momentum in the Schrödinger theory and in the Bohr model? Homework Equations ? The Attempt at a Solution Similarities: -In both theories, the principal quantum #, n, determines the...

How do you find an expression for the energy eigenvalues from the TISE (Time Indipendant Schrödinger Equation) for a given potential. e.g. why is: E = (N + 1) hbar*omega an expression for the energy eigenvalues for a potential of: V = 1/2*m*omega2x2 ?? I really have no idea where to start...

Hi, i am beginning elementary Quantum Mechanics as my course. While studying one question arise in my mind : In the solution of Schrödinger 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 Schrödinger 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 Schrödinger...

Homework Statement The solution of the Schrödinger 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 Schrödinger'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) Schrödinger'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 Schrödinger 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 Schrödinger equation, that is, second or higher powers of these quantities do not appear in the equation. Schrödinger 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 Schrödinger equation are equal to zero, and also how to prove that...

Hamilton-Jacobi Equation related to Schrödinger?? Where it comes from the Schrödinger equation? Is it related to Hamilton-Jacobi equation? And any good text to consult??

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?

Homework Statement Suppose the wave function for a particle of mass m in one dimension is psi(x)= (const)ex2/4l2 express this wave function in terms of a Fourier series or integral. I know that psi(x)=\sumk (ak *eikx) for a plane wave. I have no idea where to go from here. Any help is...

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

In quantum mechanics, time independent Schrödinger 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 Schrödinger 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 Schrödinger 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 Schrödinger 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 Schrödinger equation using the FDTD (Finite Difference Time Domain) method. The Schrödinger equation has the form dA/dz = i/2 β2 d2A/dt2 –α/2 +iγ |A2|A where β2 is dispersion, α is...