Linked Questions

43
votes
7answers
7k views

How is the Schroedinger equation a wave equation?

Wave equations take the form: $$\frac{ \partial^2 f} {\partial t^2} = c^2 \nabla ^2f$$ But the Schroedinger equation takes the form: $$i \hbar \frac{ \partial f} {\partial t} = - \frac{\hbar ^2}{...
25
votes
4answers
3k views

$\lambda=\frac{2h}{p}$ instead of $\lambda=\frac{h}{p}$?

I am studying quantum physics and there is something I don't understand: I know that for any particle $E=hf$ (Einstein relation) and $v=\lambda f$ ($v$ is the speed of the particle). I also know ...
8
votes
8answers
18k views

How to derive Schrödinger equation? [duplicate]

How is the Schrödinger equation $$ i\hbar\frac {\partial }{\partial t}\psi=H{\psi }$$ derived?
14
votes
3answers
7k views

Schrodinger's equation (explanation to non physicist)

For a report I'm writing on Quantum Computing, I'm interested in understanding a little about this famous equation. I'm an undergraduate student of math, so I can bear some formalism in the ...
8
votes
4answers
924 views

Why doesn't the Schrödinger equation contain a term of $mc^2$?

Admitting the ansatz $$ψ=e^{i(kx-ω t)} \tag{1}$$ then $$k^2=-ψ^{-1} \frac {∂^2ψ}{∂x^2} \tag{2}$$ and $$ω=iψ^{-1} \frac {∂ψ}{∂t} \tag{3}$$ If one admits that the total energy ($E$) is related to ...
14
votes
2answers
2k views

How can one find the energy eigenfunctions of a particle in a finite square well via the Klein-Gordon equation?

It is said that Klein-Gordon equation is a relativistic version of the Schrodinger equation. In Schrodinger equation, it is straightforward to include potential energy. But for K-G eqn things seem to ...
8
votes
3answers
2k views

Why is the Klein Gordon equation of second order in time?

I was wondering if there is any way to interpret the fact that the Klein Gordon equation is a 2nd order PDE in time. I mean, normally you would expect that as soon as you fix the initial wavefunction, ...
14
votes
2answers
3k views

How to derive the theory of quantum mechanics from quantum field theory?

I have read the book on quantum field theory for some time, but I still do not get the physics underline those tedious calculations. The thing confused me most is how quantum mechanics relates to ...
3
votes
1answer
1k views

Non-relativistic limit of complex scalar field

In page 42 of David Tong's lectures on Quantum Field Theory, he says that one can also derive the Schrödinger Lagrangian by taking the non-relativistic limit of the (complex?) scalar field Lagrangian. ...
3
votes
2answers
1k views

First-order and second-order wave equations, versus the uncertainty principle

In classical physics, we have second-order equations like Newton's laws, so we need to specify both position (zeroth order) and velocity (first order) of a particle as initial conditions, in order to ...
1
vote
1answer
431 views

relation between Schrodinger equation and wave equation [duplicate]

I have always been confused by the relationship between the Schrödinger equation and the wave equation. $$ i\hbar \frac{\partial \psi}{\partial t} = - \frac{\hbar^2}{2m} \nabla^2+ U \psi \hspace{0....
5
votes
3answers
525 views

Deriving Schrodinger equation from Klein-Gordon QFT with the definition $\psi(\textbf{x},t)\equiv \langle 0|\phi_0(\textbf{x},t)|\psi\rangle$

In the book "Quantum Field theory and the Standard Model" by Matthew Schwartz, page 23-24, the position space wavefunction is defined as $$\psi(x)=\langle 0|\phi(x)|\psi\rangle, \tag{2.82+2.83}$$ ...
4
votes
1answer
676 views

Non-relativistic limit in a Lagrangian density

What criteria should I consider when determining the non-relativistic limit of a Lagrangian density? For example, how would I take the non-relativistic limit of the following Lagrangian density: $$\...
2
votes
1answer
414 views

Schrödinger evolution for a Klein-Gordon equation

I have a problem with the transition from quantum relativistic wave equations (specifically Klein-Gordon equation) to QFT, since a lot of assumptions seem implicit. For example I have a problem with ...
3
votes
1answer
745 views

Non-relativistic limit of complex scalar field Lagrangian

I am trying to derive the non-relativistic Lagrangian for a complex scalar field from taking the non-relativistic limit of the complex scalar field Lagrangian. I am following the steps in "QFT for ...

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