A particle in 1D potential well

White_M
Messages
9
Reaction score
0
Hello,

What does it means when a particle having mass "m" in a one dimensional potential well has the potential given by:
V(x)=
\stackrel{-\alpha δ(x) for |x|<a}{∞ for |x|≥a}

where δ(x) is the delta function and \alpha is a constant.

I understand that the well boundries have infinite potential but what about the well? Does it have -\alpha potential only for x=0? What is the potential for |X|<a and x≠0? And how do I write the boundry conditions here?

10x!
Y.
 
Physics news on Phys.org
the potential in for X>a or X<-a is infinite
the potential on point X=0 is -infinite due to the delta function (but its integral for example is not).
the rest |X|<a and not 0, the potential is zero.

The boundary conditions on +/-a are the same (your wavefunction must vanish).
http://en.wikipedia.org/wiki/Delta_potential
 
Insights auto threads is broken atm, so I'm manually creating these for new Insight articles. Towards the end of the first lecture for the Qiskit Global Summer School 2025, Foundations of Quantum Mechanics, Olivia Lanes (Global Lead, Content and Education IBM) stated... Source: https://www.physicsforums.com/insights/quantum-entanglement-is-a-kinematic-fact-not-a-dynamical-effect/ by @RUTA
If we release an electron around a positively charged sphere, the initial state of electron is a linear combination of Hydrogen-like states. According to quantum mechanics, evolution of time would not change this initial state because the potential is time independent. However, classically we expect the electron to collide with the sphere. So, it seems that the quantum and classics predict different behaviours!

Similar threads

Back
Top