# What is Schrodinger's equation: Definition and 106 Discussions

The Schrödinger equation is a linear partial differential equation that governs the wave function of a quantum-mechanical system. It is a key result in quantum mechanics, and its discovery was a significant landmark in the development of the subject. The equation is named after Erwin Schrödinger, who postulated the equation in 1925, and published it in 1926, forming the basis for the work that resulted in his Nobel Prize in Physics in 1933.Conceptually, the Schrödinger equation is the quantum counterpart of Newton's second law in classical mechanics. Given a set of known initial conditions, Newton's second law makes a mathematical prediction as to what path a given physical system will take over time. The Schrödinger equation gives the evolution over time of a wave function, the quantum-mechanical characterization of an isolated physical system. The equation can be derived from the fact that the time-evolution operator must be unitary, and must therefore be generated by the exponential of a self-adjoint operator, which is the quantum Hamiltonian.
The Schrödinger equation is not the only way to study quantum mechanical systems and make predictions. The other formulations of quantum mechanics include matrix mechanics, introduced by Werner Heisenberg, and the path integral formulation, developed chiefly by Richard Feynman. Paul Dirac incorporated matrix mechanics and the Schrödinger equation into a single formulation. When these approaches are compared, the use of the Schrödinger equation is sometimes called "wave mechanics".

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1. ### B Particle Function? Particle Equation?

The following is the wave equation from Electrodynamics: $$\frac{\partial^2 \Psi}{\partial t^2} = c^2\frac{\partial^2 \Psi}{\partial x^2}$$ Where ##\Psi## is the wave function. But because of Heisenberg's Uncertainty, physicists had to come up with another equation (the Schrodinger equation)...
2. ### Calculate qubit states with Schrodinger's equation

Summary:: How to calculate qubit states with the Schrodinger eq I'm writing something about the relation between quantum computers and the Schrodinger equation. One of the requirements is there has to be an experiment. So I thought I could measure some qubits that have results and then do the...
3. ### I Conventional description of the matter wave

I have been working on a relatively simple problem. Just take a quantum wave function for which a physical requirement is that an arbitrary displacement of x or an arbitrary shift of t should not alter the character of the wave, and I want to find the state function solution. A possible guess...
4. ### A Interpreting QM without Schrödinger's equation

Rovelli, in his recent paper, writes: https://arxiv.org/pdf/2109.09170.pdf Do you think Rovelli is correct in implying the wave function is redundant and misleading? If we disregard the wave function's significance, beyond convenience, say we forgot it even existed, how would that change (or...
5. ### I Derivation of Schrodinger equation (chicken and egg problem?)

The classical wave equation in 1-D reads: $$\frac{\partial^2 u}{\partial x^2}(x,t) = \frac{1}{v^2}\frac{\partial^2 u}{\partial t^2}(x,t)$$ The D'alembert solution to the wave equation is: $$u(x,t) = f(x+vt) + g(x-vt)$$ so a allowed wave function solution to the 1-Dimensional classical wave...

42. ### Deriving the statistical interpretation from Schrodinger's equation?

So, there are two things in Quantum Mechanics that I understand are axioms: the first is the schrodinger equation, which cannot be derived. Okay fine, we have to start somewhere. The second axiom is that the integral from a to b of the wavefunction-mod-squared gives the probability of finding...
43. ### Where are charge and spin in Schrodinger's equation?

Schrodinger's equation is what is used to determine the probability of finding a particle somewhere, but where are charge and spin? How do you know if the probability wave you solved for is for a proton or electron or some other particle? I see m in the equation for plugging in mass, but nothing...
44. ### Proper form of schrodinger's equation?

I feel a bit silly asking this, but I've been working through some QM lately and there's one aspect of Schrodinger's equation that's puzzling me. I've typically understood the equation as i\hbar \frac{d|\psi\rangle}{dt}=\hat H |\psi\rangle, but I've also seen it written as i\hbar \frac{\partial...
45. ### Questions about Schrödinger's Equation: Help Needed!

Hi everyone I have to questions which I don't have an answer to: 1. the solution for the Schrödinger's equation are continuous (for time as well as for the location). But why do I get discrete values for the energies for example (let's say in hydrogen) ? 2. Is there a spherical harmonic...
46. ### Solving Schrödinger's Equation for Cylindrical Boundaries

Homework Statement I must get the first eigenvalues of the time independent Schrödinger's equation for a particle of mass m inside a cylinder of height h and radius a where ##h \sim a##. The boundary conditions are that psi is worth 0 everywhere on the surface of the cylinder. Homework...
47. ### Schrödinger's equation, its derivation

Richard Feynman said: So does this mean that it is a equation like the Balmer formula or the Rydberg equation? There's no theory behind it, it's just an empirical formula? Did S just look at data and come up with an equation that fit the data? Is it possible that we will find out why the...
48. ### Schrodinger's equation and the finite well(conceptual)

Hello, I have a question about Schrodinger's equation and the finite well. It isn't so much as a math question but rather how to interpret the problem. I'll use the picture on the right from here for reference and for simplicity, I'll stick to one dimension. When I think of this problem, I...
49. ### Unlocking Schrödinger's Equation Through Multivariable Calculus

I went through a whole calculus book and I didn't find anything that resembled sch eq. I specifically wanted to learn about that. What do you think the chapter will be called that introduced the math necessary for sch eq? Maybe it's in multivariable calculus.
50. ### Rest energy in Schrodinger's equation

Why is the rest energy usually ignored in Schrodinger’s equation? (I am aware of Dirac’s later relativistic equation.) What is the justification? Wouldn’t it change the nature of the solutions to the last equation below if it were included? Well, ok, it won't copy my Word equations. Why...