How to change for Postgresql the string value for json in jpa repository @Query using springboot

Maven pom dependency:

        <dependency>
            <groupId>org.postgresql</groupId>
            <artifactId>postgresql</artifactId>
            <scope>runtime</scope>
        </dependency>
        <!-- https://mvnrepository.com/artifact/org.json/json -->
        <dependency>
            <groupId>org.json</groupId>
            <artifactId>json</artifactId>
            <version>20230227</version>
        </dependency>

Configuration Dialect:

spring:
  jpa:
    properties:
      hibernate:
        dialect: org.hibernate.dialect.PostgreSQLDialect
    show-sql: 'true'
    hibernate:
      ddl-auto: update

I have the following Entity:

@Entity
@Data
@Getter
@AllArgsConstructor
@NoArgsConstructor
@Builder
@Slf4j
public class CourseEntity {
    @Id
    @GeneratedValue(strategy = GenerationType.IDENTITY)
    private Integer id;

    @Column(columnDefinition = "json")
    private String list_id_professors;
}

And the SqlCourseRepository file:

import jakarta.transaction.Transactional;
import org.springframework.data.jpa.repository.JpaRepository;
import org.springframework.data.jpa.repository.JpaSpecificationExecutor;
import org.springframework.data.jpa.repository.Modifying;
import org.springframework.data.jpa.repository.Query;
import org.springframework.data.repository.query.Param;
import org.springframework.stereotype.Repository;
import java.util.Optional;

@Repository
public interface SqlCourseRepository extends JpaRepository<CourseEntity, Integer>, JpaSpecificationExecutor {
    //multiple criteria: JpaSpecificationExecutor

    @Transactional
    @Modifying
    @Query("update CourseEntity set list_id_professors = :list_id_professors where id = :id")
    Integer updateCourseListIdProfessors(@Param(value = "id") Integer id, @Param(value = "list_id_professors") String list_id_professors);
    // If okk -> integer = num rows affected. 0 if no changes. -1 if error.
}

I have a Postgresql Database:

Postgresql Database Field Initial Value

If i want to update the JSON field, i can execute on SQL Query Tool inside the database:

update course_entity set list_id_professors = '[1,2]'::json where id = 1;

Postgresql Database Field Updated Value

My problem is how to do that on the SqlCourseRepository.

Because i cant put "::json" after the variable

Error adding "::json"

Also, another possibility is doind insted of a Json a int[] variable on the definition of the Entity’s attribute. But i have this another issue because i don’t know how to do it:

Error changing type to "Integer[]"

So i dont know how to put a SQL query that can interact with the Postgresql Database correctly