A complex scalar field that describes a quantum mechanical system. The square of the modulus of the wave function gives the probability of the system to be found in a particular state.

learn more… | top users | synonyms

2
votes
2answers
93 views

Wavefunction of isomers

In quantum chemistry, the wavefunction for a molecule can be viewed as the output of a function $\xi(m, n_1,..., n_k)$ with $m, n_i \in \mathbb{Z}^+$ that returns a $|\psi\rangle$ that satisfies a ...
1
vote
4answers
276 views

Having trouble understanding some stuff about delta functions [closed]

I was going through one of the examples in Griffith's Quantum book and there was a few things in Example 3.3 that I didn't understand that I was hoping to get some clarification on. For instance, we ...
1
vote
3answers
150 views

Variational Theorem proof

I have been trying to prove variational theorem in quantum mechanics for a couple of days but I can't understand the logic behind certain steps. Here is what I have so far: \begin{equation} ...
0
votes
1answer
83 views

Two Particle System with Identical Particles

I'm studying for an exam in quantum mechanics and tried to calculate the ground state and the first two excited states of two identical bosons (spin 0) in an infinite one dimensional potential well. ...
2
votes
2answers
91 views

Minimum information necessary to represent a pure quantum state

I was thinking about how quantum states are represented for various types of systems, and how the amount of classical information (bits) required to represent a state depends on its basis. Let's take ...
5
votes
5answers
981 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 ...
2
votes
1answer
86 views

Inconsistency in the delta potential

I encountered an inconsistency in the one-dimensional delta potential. Suppose we have a one-dimensional infinitely deep square well from $-L$ to $+L$. We know the eigenstates are sine and cosine ...
0
votes
1answer
66 views

Few particle fermion system wavefuction

Suppose I have 3 fermions($\left|\psi_1\right\rangle$, $\left|\psi_2\right\rangle$, $\left|\psi_3\right\rangle$) and a system with 3 states ( $\left|1\right\rangle$, $\left|2\right\rangle$, ...
2
votes
1answer
192 views

Normalization of a wavefunction that's superposition of two unknown energy eigenfunctions

Question:$$\psi(x)=A(3u_1(x)+4u_2(x))$$where $u_1(x)$ and $u_2(x)$ are energy eigenfunctions. How to normalize function $\psi(x)$? My intuitive solution: I got ...
0
votes
1answer
62 views

Scattering and bound States

So from my understanding, as long as $E>0$ you will have scattering states and these scattering states will always result in an imaginary $\psi$, but bound states can also have an imaginary ...
2
votes
2answers
177 views

The Delta-Function Potential

I'm reading through Griffiths Intro to QM 2nd Ed. and when it comes to bound/scattering states (2.5) they say: $E<0 \implies$ bound state $E>0 \implies$ scattering state Why doesn't this ...
1
vote
0answers
25 views

Can anyone give me a simple proof for the sign change of electronic wavefunction when taken around a loop containing a conical intersection?

How and why does the sign of the electronic wavefunction changes when it is taken around a contour? For example, suppose the initial wavefunction is $f(s;S_0)$ at nuclear configuration $S_0$ and now ...
15
votes
4answers
875 views

Why do electrons in an atom occupy only the stationary states?

When we talk about the elementary problems in quantum mechanics like particle in a box, we first calculate the energy eigen-function. Then we say that the most general state is the linear combination ...
0
votes
1answer
669 views

Ground state energies with fermions of same spin?

Consider two non-interacting Fermions (half-integer spin) confined in a 'box'. Construct the anti-symmetric wavefunctions and compare the corresponding ground-state energies of the two systems; ...
0
votes
2answers
267 views

Particle in a Box: Energy Less than the Potential Energy

I am reading quantum mechanics from Shankar's Principles of Quantum Mechanics. On page 157 he defines the box potential $V(x)$ as $$ V(x) = \left\{ \begin{array}{rl} 0 &\mbox{ if $|x|< L/2$} ...
0
votes
1answer
68 views

How can an electron be fired at a target when uncertainty principle says it will spread out around axis of motion?

Consider an electron fired at a target. Taking the axis of motion to be $x$, and position to be $(x,y,z)$ then $\Delta y = \Delta z = 0$ Therefore by the uncertainty principle $\Delta p_y = ...
1
vote
1answer
221 views

Turning a finite difference equation into code (2d Schrodinger equation)

I am trying to convert the following finite difference equations into code (taken from the bottom of page 12 of this thesis by Maike Schulte Numerical Solution of the Schrodinger Equation on Unbounded ...
2
votes
1answer
247 views

Quantum harmonic oscillator solved by analytic method using Schrödinger equation and wave function

I'm having trouble understanding the recursion formula. Using $\xi \equiv \sqrt{m\omega/\hbar}x$ and $K = 2E/\hbar\omega$, the time-independent Schrödinger equation becomes $$\frac{d^2\psi}{d\xi ^2} ...
2
votes
1answer
153 views

Kronig-Penney model

I am studying the Kronig-Penney model as treated in the book by Kittel: Introduction to Solid State Physics. In this model one considers a period potential which is zero in the region $[0,a]$ ...
1
vote
0answers
72 views

Find Equation of Motion given Hamiltonian

So I am given a harmonic oscillator in an electric field. At $t=0$, we are given that the oscillator is in the ground state. The Hamiltonian is: $$H=\hbar \omega[a^{\dagger}a+\frac12+\kappa ...
0
votes
1answer
68 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: ...
4
votes
1answer
83 views

Why can we leave off half of the general solution?

In these pdf notes, it says at the bottom of the first page and beginning of the second: [...] whose solution is: $$\Psi(\theta) = c_1 e^{i\omega\theta} + c_2 e^{-i\omega\theta}$$ Since we are ...
1
vote
1answer
178 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 ...
4
votes
2answers
349 views

Where to place the operator?

I believe it's standard to place the operator in between the conjugate of the wavefunction and the wavefunction itself. For instance, $$\langle p\rangle = \int_{-\infty}^{\infty}\Psi * ...
2
votes
2answers
289 views

Differences between wave function and set of orthonormal wave functions?

I'm reading a QM book. It first says for wave function: "The state of a physical system (or particle) is completely specified by an entity associated with it called a wave function, Ψ , that in ...
2
votes
1answer
192 views

Normalizing wavefunction

If you are trying to normalize $\psi = A\sin kx$, and you find that $|A|^2 = \frac{2}{a}$, why do you take the positive square root and not the negative? What happens if you take the negative square ...
1
vote
1answer
125 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 = ...
2
votes
1answer
111 views

On use of Hamiltonians for Helium

The Hamiltonian of helium can be expressed as the sum of two hydrogen Hamiltonians and that of the Coulomb interaction of two electrons. $$\hat H = \hat H_1 + \hat H_2 + \hat H_{1,2}.$$ The wave ...
5
votes
3answers
125 views

Is the ground state closest to the uncertainty relation? [duplicate]

For simplicity, suppose we are only talking about discrete energy levels, ie, bound state case. The energy levels are $E_1, E_2\cdots$, and the corresponding wave functions are $\psi_1, \psi_2 ...
1
vote
1answer
9k 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 Schrödinger equation for the hydrogen atom? Are there any difference between definition of the electric potential ...
1
vote
1answer
155 views

Complex Quantum Wave [closed]

Can the complex nature of quantum wave arise from the fact that particle is represented as wave packet in spatial frequency and particle's total energy is represented as wave packet in time frequency? ...
1
vote
2answers
2k views

Relation between wavenumber and propagation constant

What is the exact difference between wavenumber and propagation constant in an electromagnetic wave propagating in a medium such as a transmission line, cause i am a bit confused. Does it have to do ...
1
vote
1answer
138 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 ...
5
votes
3answers
656 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 ...
3
votes
2answers
195 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 $\vec{A}=(-\frac{1}{2}By,\frac{1}{2}Bx,0)$ ...
12
votes
4answers
433 views

Reconstruction of “wavefunction” phases from $|\psi(x)|$ and $|\tilde \psi(p)|$

Consider a "wavefunction" $\psi(x)$, which has a Fourier transform $\tilde \psi(p)$ Suppose that we know, for each $x$, $|\psi(x)|^2$, and that we know, for each $p$, $|\tilde \psi(p)|^2$. Have we ...
2
votes
0answers
36 views

How does a photon travel through an electron cloud?

We all know that the exact position and exact velocity of an electron in an atom cannot be determined simultaneously, as per the Heisenberg uncertainty principle. We only talk about the probability of ...
2
votes
5answers
693 views

Is there any operator behind probability, in quantum mechanics?

In Quantum mechanics, the probability of finding a particle at position $x$ is given by $|\psi(x)|^2$, where $\psi$ is the wave function. Wonder what is the operator which gives this probability? Is ...
0
votes
1answer
45 views

Probability to be in a particular state

If I have a wavefunction $\psi = \sum_{n=0}^{\infty} a_n e^{i \phi_n} | n \rangle$ and $(|n \rangle)$ is a set of orthonormal functions. Is it correct that the probability to be in a state $|k\rangle ...
4
votes
2answers
188 views

What is the physical reason behind linearity of Schrodinger's equation?

What is the physical reason for Schrodinger equation to be linear? Though in physics many interactions or dynamics are found non linear.
1
vote
1answer
75 views

Different mathematical methods in quantum mechanics?

My understanding is that in quantum mechanics the wavefunction may be expressed as a function or as a ket vector (composed of many orthogonal ket vectors). I'm not too sure about the further ...
2
votes
3answers
95 views

Koopmann von Neumann (KvN) Theory

I was just wondering does anyone have any informative sources apart from the obvious wikipedia articles regarding Koopmann von Neumann (KvN) theory? Or if its possible could someone explain the basic ...
7
votes
2answers
564 views

Has the collapse of wave function due to observation been recorded?

I've seen pictures like this one, which depict the outcome of the Double-slit experiment with wave-like or particle features, depending how measurement has taken place. The graphic showing ...
2
votes
2answers
264 views

Wave function for an electron in and around a small charged sphere

I am interested in solutions of the Schroedinger equation. For simplicity I started my studies with the $n=1$ ground state of the hydrogen atom. I was particularly interested in the higher moments of ...
0
votes
3answers
71 views

What does “coherent wave function of a macroscopic body” mean?

What is meant by the "coherent wave function of a macroscopic body"? I found this phrase in a paper on QM, but am unfamiliar with the terminology.
3
votes
1answer
130 views

What does the notation $\Psi_k/(\Psi_k,\Psi_k)^{1/2} $ mean?

I am currently reading the paper "Gravitation and quantum mechanics for macroscopic objects" by F. Karolyhazy (1966). In his paper, he uses certain notation that I haven't come across before (he also ...
2
votes
0answers
52 views

Relation between p+ip wave Superconductor and Moore-Read State

I am quite interested in the understanding of the relation between p_ip wave superconductor(SC) and the Moore-Read(MR) state. They share many similar properties, for example, p+ip SC has majorana as ...
1
vote
1answer
144 views

details for the double slit experiment

In the double slit experiment with electrons, are all electrons going through the slits? If the electron gun is directed between two slits, than it should hit the central part between the slits, isn't ...
1
vote
0answers
72 views

1-particle momentum eigenfunction in terms of field operator for real Klein-Gordon field

Suppose $\phi(x)$ is a real Klein-Gordon field, then the single-particle wave function $\psi(x)$ corresponding to a momentum $p$ is given by (QFT, Ryder) $$\psi_p(x)=\langle0|\phi(x)|p\rangle.$$ The ...
0
votes
1answer
53 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 ...