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.

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The Tunnelling Man [closed]

What's the probability that I will tunnel through a solid wall? By "tunnel" I mean, the probability of finding me on the other side of the wall. Assumptions Wall thickness = $d$ Clearly state any ...
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68 views

Finding the wave function of a quantum harmonic oscillator [duplicate]

How can I find the wave function of a quantum harmonic oscillator? If I measure its energy several times, my measurements will change the state of a system. All I know are the possible states, given ...
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2answers
88 views

Why is probability of finding the electron at a certain point when one of the slits is closed $|\Psi|^2 $ & not $|\Psi|^2 dx$?

Let in a given physical condition, the wave-function to a particle be assigned as $|\Psi (x_i,0,0,t)|^2 dx$. Now, at the double-slit experiment , the probability of finding the particle at any $x$ ...
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45 views

Particle in a box - speed probability distribution

Consider a particle in a box with infinite barriers. By solving the Schrödinger we can find the probability of finding the particle at some points in the box. How can we find the probability of ...
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90 views

How to measure the wave-function experimentally?

Do experimental physicists really measure the wave function of a system? How do they do it? Do they make many identically-prepared systems and measure the position of the particle(s) over and over ...
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101 views

What is the meaning of integrating over the state space?

If $\lvert\psi\rangle$ denotes the state space corresponding to a qubit, then what is the meaning of the $$\int d\psi$$ where the integral is over whole state space of a qubit? How do I evaluate it? ...
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66 views

Probability density for wavefunction given as infinite superposition of eigenstates

How do we find the probability density as a function of (x,t), if the wavefunction is expressed as an infinite superposition of eigenstates? When the wavefunction is expressed as a superpostion of ...
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64 views

Probability density for momentum in Quantum Mechanics

In a book i found the following equations: $$ \phi(k)=\frac{1}{\sqrt{2\pi}} \int_{-\infty}^\infty \Psi(x,0)e^{-ikx}dx $$ and $$ \Psi(x,t)=\frac{1}{\sqrt{2\pi}} \int_{-\infty}^\infty ...
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88 views

Problem with momentum values in a QM problem

I have the following equation of $Ψ$ around a ring (the particle is bound to move only on the ring): To visualize the state(it dies before L/2 if L=2πR): We can see from the first picture that ...
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125 views

Why “textbook examples” of solutions to Schrodinger equation only deal with electrons?

Whenever studying first courses of quantum mechanics, the Schrodinger eqaution is always illustrated by an electron in some kind of a potential, and the solution (wavefunction) represents probability. ...
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107 views

Fiber bundle understanding of the wavefunction

Usually people say that given a wavefunction $\Psi$ although $|\Psi(\cdot, t)|^2$ is the probability density for the position random variable at time $t$, the wavefunction $\Psi$ itself has no ...
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131 views

Time evolution of a wavepacket

I do not understand why if $H\psi = E\psi$, then the time-evolution of the wavefunction is given by $e^{-iEt/h}\psi(x)$.
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34 views

Molecular orbital theory

What I have learnt : When two waves overlap in phase, the resultant wave formed had a greater amplitude than that of the two interfering waves. When they overlap out of phase then the resultant ...
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122 views

What is the purpose of the imaginary portion of the wave function?

I recently watched this video. I'm trying to learn about the origin of the wave function and therefore understand its use in the Schrödinger Equation. However at the end of the video I understood up ...
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35 views

systems of particles that are not symmetric or anti-symmetric; Helium 4

Suppose I have an electron and a proton, and that the electron is in the spin-up state, and that the proton is in the spin-down state. The particles are distinguishable, so I should just be able to ...
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38 views

Applying operators to the wave function, getting the physical units

Reading the wikipedia entry about operators, in particular the table at the end listing all operators, I have several questions regarding an $N$-particle system or statements that I wonder whether ...
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60 views

Mach-Zehnder interferometry wave functions

Consider the set up below: I have read that in the apparatus the wavefunction is given by: $$|\psi \rangle=e^{i\theta}|c \rangle +i |b \rangle$$ where $\theta$ is the phase added by the phase ...
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55 views

Time dependent solution to infinite well

A particle of mass $m$ is confined within an infinite, one-dimensional potential well, $U(x)$, of width $a$. $$ U\left(x\right) = \left\{ \begin{array}{lr} \infty &\: x \leq ...
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How do I normalize this wavefunction? [closed]

I need to find the normalisation constant $A$ for the wave function: $$ \psi\left(x\right) = \left\{ \begin{array}{lr} A &\: \frac{-a}{4} \leq x \leq \frac{a}{4}\\ 0 &\: ...
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65 views

Calculating the probability of a given energy

Given a normalised wavefunction say $$\psi(x) = A\sin(n\pi x),$$ (where $A$ is a normalisation constant) I can calculate the probability of finding the particle being between a position $x$ and $x + ...
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45 views

Photograph of Light as Wave and Particle [duplicate]

what is this? actually its the first photo of light as wave and a particle. The bottom "slice" of the image shows the particles, while the top image shows light as a wave. i have questions 1.how ...
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4answers
208 views

Physical reason why the derivative of a wavefunction has to be continuous?

Question What is the physical reason (i.e. without any maths) that the derivative of a wavefunction (except with infinite potentials) has to be continuous? Other info I know that in the classical ...
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166 views

Why does the magnitude squared of the wave function give us the probability density? [duplicate]

My question doesn't go much beyond the title: Why does $$\left | \psi \left ( x,t \right ) \right |^{2}$$ give us the probability density of something appearing at a certain location? I understand ...
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131 views

Do bras and kets have dimensions?

I'm trying to understand more intuitively what bras and kets are, but some aspects of them remain a mystery to me. We usually think of $\psi (x)$ as having dimension of $[1/\sqrt{L}]$ so that ...
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Plane wave conditions

Which conditions have to be fulfilled in order to approximate a light beam by a plane wave (i.e. $\phi(x)\approx \phi(0)e^{ikx}$)? I am looking for both mathematical and experimental conditions. At ...
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Potential step and exponential decay?

Let us say we have a wave going from a region ($x<0$) where the potential is $U_1$ to a region ($x>0$) where the potential is $U_2$. The wave function in the second region takes the form: ...
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Finding the average energy from the superposition of state?

If I have two energy eigenstates $\psi_1(x)$ and $\psi_2(x)$ (corresponding to energy $E_1$ and $E_2$ respectively) and we prepare a particle in the superposition of both such that it is described by ...
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278 views

How to guarantee square integrable solutions to time-independent Schrödinger's equation?

Given the time-independent Schrödinger’s equation in one dimension $$H\psi = E\psi$$ what restrictions can we place on V(x) (inside the hamiltonian) and E to guarantee that the solutions won't have ...
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74 views

Boundary conditions of the radial Schrodinger equation

Consider the radial differential equation $$\bigg( - \frac{d^2}{dr^2} + \frac{(\ell+\frac{d-3}{2})(\ell+\frac{d-1}{2})}{r^2} + V(r) + m^2 \bigg) \phi_\ell (r) = \lambda\ \phi_\ell (r),$$ which I've ...
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112 views

What's the correct link between Dirac notation and wave mechanics integrals?

In wave mechanics when we compute the expectation value of energy we write the following $$\left<\hat{H}\right>=\int_{-\infty}^\infty\mathrm{d}x\ ...
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49 views

Quantum Physics - What is the probability of it being in specific state (Stuck on question) [closed]

The normalised wavefunction for an electron in an infinite 1D potential well of length 65 pm can be written: $$\psi=(0.038 \psi_{n=1})+(-0.227\ i \psi_{n=10})+(g \psi_{n=5}).$$ If the state is ...
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Normalizing a wave function in a mixed well

So I got this potential and want to solve for the even wavefunctions http://imgur.com/GKAy4nD Since it's symmetric around the origin I need only to look at the interval [0,b] and solve for the ...
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72 views

Orbital angular momentum of electrons

In a QM class, to study the hydrogen atom, we started by defining the Hamiltonian $H$ for a central potential, then made an orbital angular momentum operator appear as part of $H$, then down the line ...
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25 views

Scintillation from wave function

Suppose we have a system with a (non-relativistic) electron whose state is described by a time-dependent wave function $\psi(x,t)$. Then I think it's correct to say that if we introduce a phosphor ...
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49 views

Question about group velocity and travelling waves

I'm trying to learn some basic quantum mechanics and I have a question related to group velocity of a travelling wave. I know there are already a few questions related to group velocity, but I ...
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127 views

Questions about the formalism of Quantum Mechanics

I have to do a presentation on this. I'm not expected to do something really detailed, but I'm not understanding the mathematical formalism. I would like to receive general answers to these questions: ...
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What state does the particle in a box occupy?

My textbook derives the equations for the different energy states $E_n$ of the particle in a box. But my professor in class said this example was a good one because it spoke about the "superposition ...
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3answers
166 views

What is the meaning of “ Ψ is not a measurable quantity in itself”?

I want to know that why the wavefunction Ψ as a complex quantity (i.e $A+iB$ form) in quantum mechanics and somewhere I have studied that Ψ is not a measurable quantity in itself that's why we ...
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Is the Singlet state for Helium with 2 electrons symmetric rather than anti-symmetric as is meant to be for fermions?

I'm looking at two-electron Helium atoms where one electron is in the ground state (due to if it were in other states, it's de-excitation would simply lead to the ionization of the electron). The ...
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638 views

The meaning of the phase in the wave function

I have just started studying QM and I got into some trouble understanding something: Let's say there is a wave function of a particle in a 1D box ($0\leq x\leq a$): $$\psi(x,t=0) = ...
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111 views

Why is the position space free particle wavefunction a function of momentum?

This is one of those little things that has always confused me. If someone said to you "in quantum mechanics, the eigenfunctions of a free particle are $\exp(ipx/\hbar)$" how would you know that ...
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Normalizing 3-Dimensional Wave Function [closed]

How do you normalize a wave function in three dimensions with spherical coordinates?
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59 views

Free particle scattering in 2D using polar coordinates

The free particle hamiltonian commutes with the angular momentum operator L and Lz, so we can use a spherical wave basis instead of the regular plane-wave basis |k>, using spherical Bessel function ...
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100 views

Understanding the behavior of light/photons inside a Laser

I am trying to establish a model inside my head of how light behaves but find it hard with all the seemingly contradicting information. For example, electrons inside a Laser are raised to a higher ...
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2answers
47 views

What the wave function looks of a particle in the infinite square well looks like after collapse for measurements of position and energy

Consider a particle in a the infinite square well from x=0 to x=L. At t=to, I make a measurement of position and get x=L/2. What is the resulting wave function at t=to? My understanding, from reading, ...
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62 views

Normalisation of a wavefunction [closed]

If the system if found in the state: $$\psi=\sqrt{\frac{1}{2\pi}}(\frac1{\sqrt3}e^{-i3\phi}+ce^{-i4\phi})$$ what value of $c$ normalizes the wavefunction? Clearly: $$\int_0^{2\pi}\psi^*\psi ...
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Probability of finding particle in infinite square well, displaced walls

Initially a quantum particle moves in a one-dimensional well ($x$-axis) from $-a$ to $ a$, $ V = \infty $ outside and $ V = 0 $ inside the well. So initially, the wave-function $$ \psi_0 = ...
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70 views

How to separate k into real and imaginary parts?

In $k^2 - \frac{\omega^2}{c_o^2} + (\tau_{\alpha} i \omega)^{\alpha} k^2 = 0$, $k$ is the wavenumber, $\omega$ is angular frequency, others are constants. How can I separate the wavenumber $k$ into ...
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70 views

Importance of bound states

While solving a potential well problem we get scattering states and bound states (if exist). Number of the bound states we get depends on the potential profile. What I want to ask is, what is the ...
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Quantum Mechanics Notation

Generally we have that $$|\psi\rangle=\int_{all space} \psi(\mathbf x)|\mathbf x\rangle d^3\mathbf x$$ and therefore $\psi(\mathbf x)=\langle\mathbf x|\psi\rangle$. When discussing the mutual ...