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Results tagged with potential
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user 97407
Scalar and vector potentials in electromagnetism. The scalar potential is potential energy per unit charge. For potential energy, use the [potential-energy] tag.
0
votes
1
answer
278
views
Non-dimensionalize Schroedinger's equation for this potential
I am having trouble non-dimensionalize this S.E. in order to solve numerically.. the potential is
$$V(x)=-V_{0}/(1+x^2/L^2)$$
we know that $A = V_{0}/\hbar \omega$ is dimensionless, and $B = E/\hbar …
- 81
2
votes
0
answers
719
views
Guess the wave function in a given potential
Are there any techniques in guessing the ground state wave function in any given potential?
For example, for a given potential like $$ \frac{1}{1-x^2}$$ or $$ \frac{1}{1-x^3}~? …
- 81
2
votes
1
answer
326
views
Superpotential for Gaussian potential well? [closed]
so I am looking for the super potential of a Gaussian well, namely $V= -e^{-x^2/2}$, and the super potential has to satisfy the Riccati equation,$
− W′ ( x ) + W ( x ) = V ( x ) − a$. …
- 81
4
votes
1
answer
2k
views
How do we find the number of bounded states in this potential?
for the potential
$$V(x)=-\frac{1}{1+\frac{x^2}{m^2}}$$
we can approximate the wave function and bounded state accurately for $x << m$ as simple harmonic oscillator, so what are we gonna do if $x$ is … Is it the number of bounded state in this exact potential is no more than the bound state energy that is great than 0? How do we find the exact number? …
- 81