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Time-independent Schrödinger equation for a free one dimensional particle
Ciro Santilli
(
@cirosantilli,
37
)
...
Particle physics
Quantum mechanics
Non-relativistic quantum mechanics
Schrödinger equation
Solutions of the Schrodinger equation
Schrödinger equation for a free one dimensional particle
Updated
2025-07-16
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∂
x
2
∂
2
ψ
(
x
)
=
−
ℏ
2
2
m
E
ψ
(
x
)
(1)
so the solution is:
ψ
(
x
)
=
e
ℏ
2
m
E
i
x
(2)
We
notice that the solution has
continuous spectrum
, since any value of
E
can provide
a
solution.
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Schrödinger equation for a free one dimensional particle
Solutions of the Schrodinger equation
Schrödinger equation
Non-relativistic quantum mechanics
Quantum mechanics
Particle physics
Physics
Natural science
Science
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