Study on Pentaqaurks by Solving Schrodinger Equation in the Non-Hermitian Quantum Mechanics

The interaction of the charmed baryon and the anticharmed meson is assumed to be realized by exchanging a scalar meson of $f_0(500)$, and then these systems are studied by solving the Schrodinger equation, respectively. When the pentaquarks $P_{c\bar{c}}(4312)^{+}$, $P_{c\bar{c}}(4457)^{+}$, $P_{c\bar{c}s}(4338)^0$, and $P_{c\bar{c}s}(4459)^{0}$ are treated as $\Sigma_c \bar{D}$, $\Sigma_c \bar{D}^*$, $\Xi_c \bar{D}$ and $\Xi_c \bar{D}^*$ bound states, four resonance states of them are obtained as solutions of the Schrodinger equation under the outgoing wave condition, respectively. The resonance state of $\Sigma_c \bar{D}$ might correspond to the particle $P_{c\bar{c}}(4440)^{+}$, while the other three resonance states have no counterparts in the review of the Particle Data Group(PDG). Although the binding energy of the bound state is only several MeVs, all these resonance states are more than 100 MeV higher than their corresponding thresholds, respectively. The calculation results indicate that the spectrums of the strange and non-strange pentaquarks are symmetric to each other.