# Tagged Questions

32 views

### Correct approach for calculating excited states of circular quantum dot under effective mass approximation

From Asnani, Mahajan et al, Pramana Journal Of Physics 73 #3 (2009) p574-580 "Effective mass theory of a two-dimensional quantum dot in the presence of magnetic field", which can be seen here: ...
140 views

### Particle Outside the Box

What prohibits, mathematically, that a particle cannot be found outside the box ? Here, I am referring to particle in a box problem (infinite potential on both ends & zero potential along the ...
121 views

### Is there only radial motion in the Hydrogen ground state?

The ground state of the Hydrogen atom is spherically symmetric. In other words, the wave function Psi depends only on the distance r of the electron from the nucleus. As a consequence all ...
104 views

### What is the difference between the Bohr model of the atom and Schrödinger's model?

What is the difference between the Bohr model of the atom and The solution of the SchrÃ¶dinger equation for the hydrogen atom? Are there any difference between definition of the electric potential ...
50 views

### Degeneracy in One Dimension

I'm reading this wikipedia article and I'm trying to understand the proof under "Degeneracy in One Dimension". Here's what it says: Considering a one-dimensional quantum system in a potential ...
130 views

### Infinitely many degeneracy of Landau level: Countable or Uncountable?

Description of Landau levels can be found in many standard textbooks of quantum mechanics and here. Two ubiquitous solutions apply either the symmetric gauge $\vec{A}=(-\frac{1}{2}By,\frac{1}{2}Bx,0)$ ...
269 views

### What does the Schrodinger Equation really mean?

I understand that the Schrodinger equation is actually a principle that cannot be proven. But can someone give a plausible foundation for it and give it some physical meaning/interpretation. I guess ...
315 views

### Am I missing a trick to solving this differential equation?

I was playing around with a 3-D potential $V$ such that $V_{(r)} = 0$ for $r<a$, and $V_{(r)} = V_0$ otherwise. By using the SchrÃ¶dinger Equation, I showed that: ...
107 views

### Doubt in a certain equation of a research paper [closed]

In the given paper, I am stuck at equation (7). The equation that I am trying to solve for particle outside the well is : (1/g)*(g'') + (1/(r*g))*g' - (k_o)^2 = 0 where g = Radial wave function. r = ...
37 views

### Expected value $<\hat{x}>$ of: $\Phi(x,t)=Ne^{-a[(Mx^2/\hbar)+it]}$ is infinite, why?

The problem says: A particle of mass $M$ is described by the wave function: $$\Phi(x,t)=Ne^{-a[(Mx^2/\hbar)+it]}$$ where a is a positive constant. Asked to determine such things as the ...
64 views

185 views

### Harmonic Oscillator potential, proof that Gaussians remain Gaussians?

I read in several papers that for a Harmonic Oscillator Hamiltonian in the time dependent SchrÃ¶dinger equation a Gaussian wave packet remains Gaussian. Unfortunately I could not find any proof for ...
258 views

93 views

### Particle in a higher-dimensional box with an attractive delta potential

Suppose you have a particle in the box $[0,L]^d$, with an attractive Dirac delta potential $-\delta_{\vec w}(x)$ at $\vec w$. How do you solve the Schroedinger equation for this system? In the case ...
112 views

### Infinite well particle subject to additional time dep. potential

I am asked to find the wavefunction of the particle in a well subject to an additional potential $$V(x,t)=\frac{\pi x \hbar}{L}\delta(t).$$ I have already solved that ...
257 views

### Non-separable solution for the Schrödinger equation

SchrÃ¶dinger solutions are usually if not always of the type: $\psi=\operatorname{T}(t)*\operatorname{X}(x)$ (we use the separation of variables method to arrive at the time independent Schroedinger ...
297 views

### Solving quantum radial equation for infinite potential spherical annulus for $l=0$

There is a mass $m$ in a potential such that $$V(r) = \left\{ \begin{array}{lr} 0, & a \leq r \leq b\\ \infty, & \text{everywhere else} \end{array} \right.$$ ...
170 views

### Virial theorem and variational method: an exercise (re-edited)

I have a hydrogen atom, knowing that its Hamiltonian has been modified turning the standard potential $$V_{0}(r) = -\frac{Z}{r}$$ into $$V(r) = -\frac{g}{r^{\frac{3}{2}}}$$ with $g$ a positive ...
150 views

771 views

### Infinite Wells and Delta Functions

In considering a delta potential barrier in an infinite well, I can just enforce continuity at the potential barrier-it doesn't have to go to zero. Why then does it need to go to zero at the walls of ...
441 views

### Why is the wave function complex? [duplicate]

Why should an equation (TDSE) in which first time derivative is related to second space derivative have a solution that contains $i$?The wave function is supposed to be complex, but I am unable to ...
193 views

### In Schrödinger equation, can we get $\Psi$ if we know $\varphi(n)$?

Let $A$ be a mechanical quantity and we know its eigenfunction $\varphi(n)$. Can we get its wave function $\Psi$, if we measure $A$ for many (maybe infinite) times at the same time?
311 views

### Tunnelling through a Dirac potential barrier

I am reading a QM book by Griffiths, which says it is possible for wave particle to tunnel through a barrier formulated by a Dirac function. This function is known to peak at infinity and also ...