∂ Ψ ∂ t = − i E ℏ A e i ( p ⋅ r − E t ) / ℏ = − i E ℏ Ψ

A
Thread starter Aga33
Start date Oct 18, 2016

In summary, the equation ∂ Ψ ∂ t = − i E ℏ A e i ( p ⋅ r − E t ) / ℏ represents the time-dependent Schrödinger equation, which is a fundamental equation in quantum mechanics. It is used to calculate the time evolution of a quantum system and make predictions about its behavior. The symbols in the equation have specific meanings in the context of quantum mechanics, and the complex number i allows for the description of quantum phenomena. Other forms of the Schrödinger equation exist for different types of systems.

Oct 18, 2016

Aga33

Hi - I've been given this to "solve". Now I don't even know where to start with understanding what it's about and didn't know where else to turn to. If anyone could give me a nudge I'd be most grateful.

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Oct 18, 2016

BvU

Science Advisor

Homework Helper

Ha Aga,

It's called the Schroedinger equation, which google.

Oct 18, 2016

Aga33

Thanks, BvU, you're my star!

FAQ: ∂ Ψ ∂ t = − i E ℏ A e i ( p ⋅ r − E t ) / ℏ = − i E ℏ Ψ

What does the equation ∂ Ψ ∂ t = − i E ℏ A e i ( p ⋅ r − E t ) / ℏ represent?

The equation represents the time-dependent Schrödinger equation, which is a fundamental equation in quantum mechanics. It describes how the wave function, Ψ, of a quantum system changes over time.

What do the symbols in the equation ∂ Ψ ∂ t = − i E ℏ A e i ( p ⋅ r − E t ) / ℏ stand for?

The symbols have specific meanings in the context of quantum mechanics. ∂ Ψ ∂ t represents the change in the wave function with respect to time, E is the energy of the system, ℏ is the reduced Planck's constant, A is a constant, p is the momentum of the system, r is the position, and t is time.

How is the equation ∂ Ψ ∂ t = − i E ℏ A e i ( p ⋅ r − E t ) / ℏ used in quantum mechanics?

The equation is used to calculate the time evolution of a quantum system. By solving the equation, we can determine the wave function at any given time and make predictions about the behavior of the system.

What is the significance of the complex number in the equation ∂ Ψ ∂ t = − i E ℏ A e i ( p ⋅ r − E t ) / ℏ?

The complex number, i, represents the imaginary unit in mathematics. In quantum mechanics, the wave function is a complex-valued function, and the imaginary part of the equation allows for the description of quantum phenomena such as interference and superposition.

Are there any other forms of the Schrödinger equation?

Yes, there is also a time-independent Schrödinger equation, which does not include the term for time. This is used to describe stationary states of a quantum system. There are also other forms of the equation for different types of systems, such as the Klein-Gordon equation for relativistic particles and the Dirac equation for spin-1/2 particles.