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Results tagged with wavefunction
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user 328424
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. DO NOT USE THIS TAG for classical waves.
1
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1
answer
537
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Schrödinger equation obtain $ψ(x,t)$ from $ψ(x,0)$
In this answer of the post "Wave packet expression and Fourier transforms" it is said that for the S.E. we have this property:
If we start with an initial profile $ψ(x,0)=e^{ikx}$, then the solution …
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2
votes
1
answer
754
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Wave function Fourier transform with time
I found the Fourier transform at $t=0$ for the wave function of a wave packet (and it's inverse Fourier transform) :
$$\Psi(x,0)=\frac{1}{\sqrt{2\pi}}\int_{-\infty}^{\infty}\Phi(k)e^{ikx}dk$$
$$\Phi(k …
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3
votes
Accepted
Doubt in the bound states which we get through Levinson's Theorem
Yes, in fact there is a way to prove it: by placing a Hard Wall at some distance L on the right. Doing so, allows to count the scattering states (as the system becomes a sort of infinite square well). …
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4
votes
1
answer
92
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Levinson's theorem counting bound states negatively
The Levinson's theorem states that the number of bound states $N_b$ is $$ N_b = \frac{1}{\pi} (\delta (0) - \delta (\infty)).$$
My question is: can this number be negative? For example if the potenti …
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0
votes
1
answer
128
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Superposition of momentum plane waves for a WF: discrete of continuous?
On the one hand there is a theorem that states that any reasonable wave function $\Psi$ can be written as a superposition of eigenstates of $\hat Q$ (a hermitian operator).
So if $\Psi _i$ are the eig …
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1
vote
1
answer
137
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1D bound state for a real potential
So $\Psi \equiv \Psi_{real} +i\Psi_{imaginary}=\Psi_{real} (1+ic)=(1+c^2)e^{iArg(1+ic)}\Psi_{real}$
Whatever the proof, I don't understand the statement since any complex number (the wavefunction is one …
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0
votes
0
answers
41
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Eigenstates of $L^2$ and $L_z$ no $r$ dependence Why? [duplicate]
Does anybody know why the eigenstates common to the casimir operator $L^2$ and the $z$-axis angular momentum $L_z$ have no $r$ dependence (they are written $\psi_{m,l} (\theta, \phi)$)?
Is it because …
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4
votes
2
answers
290
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Applying measurement postulate to a continuous sum of eigenvectors (by analogy)
Measurement postulate:
If we measure the Hermitian operator $\hat Q$ in the state $Ψ$, the possible
outcomes for the measurement are the eigenvalues $q_1$, $q_2$, . . .. The probability $p_i$ to meas …
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2
votes
1
answer
100
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Complex $\Phi$ to prove the group velocity of a wavepacket
Barton Zwiebach from the physics department of M.I.T., Course: 8.04 'Quantum Physics I', title: de Broglie Wavelength and Galilean Transformations, Phase and Group Velocities, Choosing the Wavefunction …
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