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 Yearling
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  • 37 votes cast
Dec
4
comment How do we find the number of bounded states in this potential?
@Praan: I would argue that it is a bit simplified to think that for $x_0\to 0$ you get a delta function. It is the fact that the potential approaches 0 for $x\to \infty$ only like $1/x^2$ that allows for an infinity of bound states. A "true" delta function would approach 0 faster (already for $1/x^4$ you get a finite number of bound states).
Dec
4
comment How do we find the number of bounded states in this potential?
@tjkt: call WKB in this context Bohr-Sommerfeld quantization and you might be familiar with that. If numerics only gives you 4 eigenvalues, then the numerics is wrong. You did not specify the Hamiltonian nor the Hilbert space though. I did assume you want to solve Schrödinger's equation on $x\in \mathbb{R}$...
Dec
4
comment How do we find the number of bounded states in this potential?
Note that in a potential $-1/(x^4+1)$ the number of states would be finite though...
Dec
4
answered How do we find the number of bounded states in this potential?
Dec
3
comment What's the formula to determine how fast a magnet can travel and still hold objects in it's magnetic field?
I guess you are asking for the acceleration. The velocity does not matter because of relativity...
Nov
1
comment Why is the change in entropy greater for processes occurring at lower temperatures?
In many cases, this formula (or the equivalent in terms of Carnot processes) is taken as the definition of (absolute) temperature. If you want an explanation of this formula, you have to tell us how you want to define temperature in the first place...
Sep
19
comment Spontaneous radiative decay due to electric dipole radiation
Also fixed that.
Sep
19
revised Spontaneous radiative decay due to electric dipole radiation
added 5 characters in body
Sep
7
comment Spontaneous radiative decay due to electric dipole radiation
@SaschaFrölich: I have fixed that.
Sep
7
revised Spontaneous radiative decay due to electric dipole radiation
added 11 characters in body
Sep
3
answered Spontaneous radiative decay due to electric dipole radiation
May
26
comment Addition of 3 angular momenta
You seem to be forgetting Pauli's principle...
Apr
22
comment Is the Landau Free Energy U-TS or βH?
No, I mean the fact that calculating the log of the partition function gives $U - T S$, so no just the mean energy $U$ but also the entropy term.
Apr
22
comment Is the Landau Free Energy U-TS or βH?
Do you understand why $F= - T \ln Z$, with $Z=\mathop{\rm tr} e^{-H/T}$?
Apr
6
awarded  Yearling
Jan
17
comment Klein-Gordon field commutator integral identity
@spitespike: if the integral is taken over $\mathbb{R}^3$ the result quoted is wrong...
Jan
16
comment Klein-Gordon field commutator integral identity
You posted the same question on math.stackexchange. You should only post it to one of the sites. As I have explained there, there is something seriously wrong with your first formula as the term in the bracket simply vanishes. Furthermore, the integral over $k$ should be in 2d.
Jan
11
comment Harmonic oscillator coherent state expected values
The energy is conserved...
Nov
21
comment Does the $\bf{1+3}$ representation of $SU(2)$ also represent $SU(2)\times SU(2)$?
@Lior: I'm not sure I understand your statement. Typically in quantum mechanics one looks at the action of $S= S_1 +S_2$ to determine which spin the tensor product states $|m_1,m_2\rangle$ have. This corresponds due to $\exp(S) = \exp(S_1)\otimes \exp(S_2)$ to simultaneously rotating both spins.
Nov
21
comment Does the $\bf{1+3}$ representation of $SU(2)$ also represent $SU(2)\times SU(2)$?
@Lior: if the two spins are unrelated the representation does not factor into 1+3 but it is irreducible itself.