the allowed energy status of a free particles are
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For the free particle, the absence of confinement allowed an energy continuum. Note that, in both cases, the number of energy levels is infinite-denumerably infinite for the particle in a box, but nondenumerably infinite for the free particle. The state of lowest energy for a quantum system is termed its ground state.
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we no that the normalization of of a state of a free particle is indeterminate and therefore it does not have any physical state or definite energy. On the other hand, let's consider a free particle of wave function sin Kx . The energy of the state can be written as, h2k2/2m. Since , the the energy of the state is not k dependent, therefore we can say from the energy Equation, Energy of a state is definite.
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